التوافيق ببساطة

# التوافيق ببساطة

ما هي التوافيق؟

التوافيق (Combinations) هي اختيار مجموعة صغيرة من مجموعة أكبر **دون الاهتمام بالترتيب**.

أي أن تغيير ترتيب العناصر لا ينتج مجموعة جديدة.

---

متى نستخدم التوافيق؟

نستخدم التوافيق عندما:

- نختار عناصر من مجموعة أكبر. - لا يهم ترتيب العناصر المختارة.

---

مثال

لدينا دوري يضم خمسة منتخبات:

- السعودية - مصر - الجزائر - العراق - الأردن

ونريد أن يلعب كل فريق مع كل فريق آخر **مرة واحدة فقط**.

السؤال:

كم مباراة ستقام؟

---

لماذا نستخدم التوافيق؟

لأن ترتيب الفريقين لا يغير المباراة.

مثلاً:

- السعودية × مصر

هي نفسها:

- مصر × السعودية

إذن **الترتيب غير مهم**، لذلك نستخدم **التوافيق**.

---

قانون التوافيق

<div class="math-display" style="text-align:center;margin:10px 0;direction:ltr;overflow-x:auto;max-width:100%;"><svg aria-label="C(n,r)=\frac{n!}{r!(n-r)!}" data-tex="C(n,r)=\frac{n!}{r!(n-r)!}" style="display:block;margin:0 auto;vertical-align: -2.172ex;" xmlns="http://www.w3.org/2000/svg" width="20.058ex" height="5.321ex" role="img" focusable="false" viewBox="0 -1392 8865.7 2352" xmlns:xlink="http://www.w3.org/1999/xlink"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D436" xlink:href="#MJXG-TEX-I-1D436"></use></g><g data-mml-node="mo" transform="translate(760,0)"><use data-c="28" xlink:href="#MJXG-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(1149,0)"><use data-c="1D45B" xlink:href="#MJXG-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(1749,0)"><use data-c="2C" xlink:href="#MJXG-TEX-N-2C"></use></g><g data-mml-node="mi" transform="translate(2193.7,0)"><use data-c="1D45F" xlink:href="#MJXG-TEX-I-1D45F"></use></g><g data-mml-node="mo" transform="translate(2644.7,0)"><use data-c="29" xlink:href="#MJXG-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(3311.4,0)"><use data-c="3D" xlink:href="#MJXG-TEX-N-3D"></use></g><g data-mml-node="mfrac" transform="translate(4367.2,0)"><g data-mml-node="mrow" transform="translate(1810.2,676)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJXG-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(600,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g></g><g data-mml-node="mrow" transform="translate(220,-710)"><g data-mml-node="mi"><use data-c="1D45F" xlink:href="#MJXG-TEX-I-1D45F"></use></g><g data-mml-node="mo" transform="translate(451,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g><g data-mml-node="mo" transform="translate(729,0)"><use data-c="28" xlink:href="#MJXG-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(1118,0)"><use data-c="1D45B" xlink:href="#MJXG-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(1940.2,0)"><use data-c="2212" xlink:href="#MJXG-TEX-N-2212"></use></g><g data-mml-node="mi" transform="translate(2940.4,0)"><use data-c="1D45F" xlink:href="#MJXG-TEX-I-1D45F"></use></g><g data-mml-node="mo" transform="translate(3391.4,0)"><use data-c="29" xlink:href="#MJXG-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(3780.4,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g></g><rect width="4258.4" height="60" x="120" y="220"></rect></g></g></g></svg></div>

حيث:

- **n** = عدد العناصر الكلي. - **r** = عدد العناصر المختارة. - **!** تعني المضروب (Factorial).

---

تطبيق المثال

لدينا:

- n = 5 - r = 2

نعوض في القانون:

<div class="math-display" style="text-align:center;margin:10px 0;direction:ltr;overflow-x:auto;max-width:100%;"><svg aria-label="C(5,2)=\frac{5!}{2!(5-2)!}" data-tex="C(5,2)=\frac{5!}{2!(5-2)!}" style="display:block;margin:0 auto;vertical-align: -2.172ex;" xmlns="http://www.w3.org/2000/svg" width="19.938ex" height="5.321ex" role="img" focusable="false" viewBox="0 -1392 8812.7 2352" xmlns:xlink="http://www.w3.org/1999/xlink"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D436" xlink:href="#MJXG-TEX-I-1D436"></use></g><g data-mml-node="mo" transform="translate(760,0)"><use data-c="28" xlink:href="#MJXG-TEX-N-28"></use></g><g data-mml-node="mn" transform="translate(1149,0)"><use data-c="35" xlink:href="#MJXG-TEX-N-35"></use></g><g data-mml-node="mo" transform="translate(1649,0)"><use data-c="2C" xlink:href="#MJXG-TEX-N-2C"></use></g><g data-mml-node="mn" transform="translate(2093.7,0)"><use data-c="32" xlink:href="#MJXG-TEX-N-32"></use></g><g data-mml-node="mo" transform="translate(2593.7,0)"><use data-c="29" xlink:href="#MJXG-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(3260.4,0)"><use data-c="3D" xlink:href="#MJXG-TEX-N-3D"></use></g><g data-mml-node="mfrac" transform="translate(4316.2,0)"><g data-mml-node="mrow" transform="translate(1859.2,676)"><g data-mml-node="mn"><use data-c="35" xlink:href="#MJXG-TEX-N-35"></use></g><g data-mml-node="mo" transform="translate(500,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g></g><g data-mml-node="mrow" transform="translate(220,-710)"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJXG-TEX-N-32"></use></g><g data-mml-node="mo" transform="translate(500,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g><g data-mml-node="mo" transform="translate(778,0)"><use data-c="28" xlink:href="#MJXG-TEX-N-28"></use></g><g data-mml-node="mn" transform="translate(1167,0)"><use data-c="35" xlink:href="#MJXG-TEX-N-35"></use></g><g data-mml-node="mo" transform="translate(1889.2,0)"><use data-c="2212" xlink:href="#MJXG-TEX-N-2212"></use></g><g data-mml-node="mn" transform="translate(2889.4,0)"><use data-c="32" xlink:href="#MJXG-TEX-N-32"></use></g><g data-mml-node="mo" transform="translate(3389.4,0)"><use data-c="29" xlink:href="#MJXG-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(3778.4,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g></g><rect width="4256.4" height="60" x="120" y="220"></rect></g></g></g></svg></div>

<div class="math-display" style="text-align:center;margin:10px 0;direction:ltr;overflow-x:auto;max-width:100%;"><svg aria-label="=\frac{5!}{2!\times3!}" data-tex="=\frac{5!}{2!\times3!}" style="display:block;margin:0 auto;vertical-align: -1.602ex;" xmlns="http://www.w3.org/2000/svg" width="9.67ex" height="4.751ex" role="img" focusable="false" viewBox="0 -1392 4274.2 2100" xmlns:xlink="http://www.w3.org/1999/xlink"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mo"><use data-c="3D" xlink:href="#MJXG-TEX-N-3D"></use></g><g data-mml-node="mfrac" transform="translate(1055.8,0)"><g data-mml-node="mrow" transform="translate(1220.2,676)"><g data-mml-node="mn"><use data-c="35" xlink:href="#MJXG-TEX-N-35"></use></g><g data-mml-node="mo" transform="translate(500,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g></g><g data-mml-node="mrow" transform="translate(220,-686)"><g data-mml-node="mn"><use data-c="32" xlink:href="#MJXG-TEX-N-32"></use></g><g data-mml-node="mo" transform="translate(500,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g><g data-mml-node="mo" transform="translate(1000.2,0)"><use data-c="D7" xlink:href="#MJXG-TEX-N-D7"></use></g><g data-mml-node="mn" transform="translate(2000.4,0)"><use data-c="33" xlink:href="#MJXG-TEX-N-33"></use></g><g data-mml-node="mo" transform="translate(2500.4,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g></g><rect width="2978.4" height="60" x="120" y="220"></rect></g></g></g></svg></div>

نعرف أن:

- 5! = 120 - 3! = 6 - 2! = 2

إذن:

<div class="math-display" style="text-align:center;margin:10px 0;direction:ltr;overflow-x:auto;max-width:100%;"><svg aria-label="\frac{120}{6\times2} = \frac{120}{12} = 10" data-tex="\frac{120}{6\times2} = \frac{120}{12} = 10" style="display:block;margin:0 auto;vertical-align: -1.602ex;" xmlns="http://www.w3.org/2000/svg" width="18.709ex" height="4.638ex" role="img" focusable="false" viewBox="0 -1342 8269.6 2050" xmlns:xlink="http://www.w3.org/1999/xlink"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mfrac"><g data-mml-node="mn" transform="translate(581.2,676)"><use data-c="31" xlink:href="#MJXG-TEX-N-31"></use><use data-c="32" xlink:href="#MJXG-TEX-N-32" transform="translate(500,0)"></use><use data-c="30" xlink:href="#MJXG-TEX-N-30" transform="translate(1000,0)"></use></g><g data-mml-node="mrow" transform="translate(220,-686)"><g data-mml-node="mn"><use data-c="36" xlink:href="#MJXG-TEX-N-36"></use></g><g data-mml-node="mo" transform="translate(722.2,0)"><use data-c="D7" xlink:href="#MJXG-TEX-N-D7"></use></g><g data-mml-node="mn" transform="translate(1722.4,0)"><use data-c="32" xlink:href="#MJXG-TEX-N-32"></use></g></g><rect width="2422.4" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(2940.2,0)"><use data-c="3D" xlink:href="#MJXG-TEX-N-3D"></use></g><g data-mml-node="mfrac" transform="translate(3996,0)"><g data-mml-node="mn" transform="translate(220,676)"><use data-c="31" xlink:href="#MJXG-TEX-N-31"></use><use data-c="32" xlink:href="#MJXG-TEX-N-32" transform="translate(500,0)"></use><use data-c="30" xlink:href="#MJXG-TEX-N-30" transform="translate(1000,0)"></use></g><g data-mml-node="mn" transform="translate(470,-686)"><use data-c="31" xlink:href="#MJXG-TEX-N-31"></use><use data-c="32" xlink:href="#MJXG-TEX-N-32" transform="translate(500,0)"></use></g><rect width="1700" height="60" x="120" y="220"></rect></g><g data-mml-node="mo" transform="translate(6213.8,0)"><use data-c="3D" xlink:href="#MJXG-TEX-N-3D"></use></g><g data-mml-node="mn" transform="translate(7269.6,0)"><use data-c="31" xlink:href="#MJXG-TEX-N-31"></use><use data-c="30" xlink:href="#MJXG-TEX-N-30" transform="translate(500,0)"></use></g></g></g></svg></div>

إذن عدد المباريات هو:

**10 مباريات.**

---

معنى المضروب (Factorial)

المضروب هو حاصل ضرب العدد في جميع الأعداد الصحيحة الأصغر منه حتى 1.

أمثلة:

- 5! = 5 × 4 × 3 × 2 × 1 = 120 - 4! = 24 - 3! = 6 - 2! = 2 - 1! = 1 - 0! = 1

---

أمثلة أخرى

### اختيار 3 طلاب من بين 10

<div class="math-display" style="text-align:center;margin:10px 0;direction:ltr;overflow-x:auto;max-width:100%;"><svg aria-label="C(10,3)" data-tex="C(10,3)" style="display:block;margin:0 auto;vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="7.879ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3482.7 1000" xmlns:xlink="http://www.w3.org/1999/xlink"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D436" xlink:href="#MJXG-TEX-I-1D436"></use></g><g data-mml-node="mo" transform="translate(760,0)"><use data-c="28" xlink:href="#MJXG-TEX-N-28"></use></g><g data-mml-node="mn" transform="translate(1149,0)"><use data-c="31" xlink:href="#MJXG-TEX-N-31"></use><use data-c="30" xlink:href="#MJXG-TEX-N-30" transform="translate(500,0)"></use></g><g data-mml-node="mo" transform="translate(2149,0)"><use data-c="2C" xlink:href="#MJXG-TEX-N-2C"></use></g><g data-mml-node="mn" transform="translate(2593.7,0)"><use data-c="33" xlink:href="#MJXG-TEX-N-33"></use></g><g data-mml-node="mo" transform="translate(3093.7,0)"><use data-c="29" xlink:href="#MJXG-TEX-N-29"></use></g></g></g></svg></div>

يمثل عدد الطرق لاختيار ثلاثة طلاب دون الاهتمام بترتيبهم.

---

### اختيار لجنة من 5 أشخاص من بين 20

<div class="math-display" style="text-align:center;margin:10px 0;direction:ltr;overflow-x:auto;max-width:100%;"><svg aria-label="C(20,5)" data-tex="C(20,5)" style="display:block;margin:0 auto;vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="7.879ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 3482.7 1000" xmlns:xlink="http://www.w3.org/1999/xlink"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D436" xlink:href="#MJXG-TEX-I-1D436"></use></g><g data-mml-node="mo" transform="translate(760,0)"><use data-c="28" xlink:href="#MJXG-TEX-N-28"></use></g><g data-mml-node="mn" transform="translate(1149,0)"><use data-c="32" xlink:href="#MJXG-TEX-N-32"></use><use data-c="30" xlink:href="#MJXG-TEX-N-30" transform="translate(500,0)"></use></g><g data-mml-node="mo" transform="translate(2149,0)"><use data-c="2C" xlink:href="#MJXG-TEX-N-2C"></use></g><g data-mml-node="mn" transform="translate(2593.7,0)"><use data-c="35" xlink:href="#MJXG-TEX-N-35"></use></g><g data-mml-node="mo" transform="translate(3093.7,0)"><use data-c="29" xlink:href="#MJXG-TEX-N-29"></use></g></g></g></svg></div>

لأن ترتيب أعضاء اللجنة لا يهم.

---

# الفرق بين التوافيق والتباديل

| المقارنة | التوافيق | التباديل | |-----------|----------|----------| | هل الترتيب مهم؟ | ❌ لا | ✅ نعم | | القانون | <span class="math-inline" dir="ltr" style="display:inline-block;direction:ltr;unicode-bidi:isolate;vertical-align:baseline;white-space:nowrap;margin:0 2px;"><svg aria-label="C(n,r)=\frac{n!}{r!(n-r)!}" data-tex="C(n,r)=\frac{n!}{r!(n-r)!}" style="display:inline-block;vertical-align: -1.238ex;" xmlns="http://www.w3.org/2000/svg" width="16.658ex" height="3.275ex" role="img" focusable="false" viewBox="0 -900.3 7362.7 1447.4" xmlns:xlink="http://www.w3.org/1999/xlink"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D436" xlink:href="#MJXG-TEX-I-1D436"></use></g><g data-mml-node="mo" transform="translate(760,0)"><use data-c="28" xlink:href="#MJXG-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(1149,0)"><use data-c="1D45B" xlink:href="#MJXG-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(1749,0)"><use data-c="2C" xlink:href="#MJXG-TEX-N-2C"></use></g><g data-mml-node="mi" transform="translate(2193.7,0)"><use data-c="1D45F" xlink:href="#MJXG-TEX-I-1D45F"></use></g><g data-mml-node="mo" transform="translate(2644.7,0)"><use data-c="29" xlink:href="#MJXG-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(3311.4,0)"><use data-c="3D" xlink:href="#MJXG-TEX-N-3D"></use></g><g data-mml-node="mfrac" transform="translate(4367.2,0)"><g data-mml-node="mrow" transform="translate(1187.3,394) scale(0.707)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJXG-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(600,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g></g><g data-mml-node="mrow" transform="translate(220,-370.3) scale(0.707)"><g data-mml-node="mi"><use data-c="1D45F" xlink:href="#MJXG-TEX-I-1D45F"></use></g><g data-mml-node="mo" transform="translate(451,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g><g data-mml-node="mo" transform="translate(729,0)"><use data-c="28" xlink:href="#MJXG-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(1118,0)"><use data-c="1D45B" xlink:href="#MJXG-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(1718,0)"><use data-c="2212" xlink:href="#MJXG-TEX-N-2212"></use></g><g data-mml-node="mi" transform="translate(2496,0)"><use data-c="1D45F" xlink:href="#MJXG-TEX-I-1D45F"></use></g><g data-mml-node="mo" transform="translate(2947,0)"><use data-c="29" xlink:href="#MJXG-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(3336,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g></g><rect width="2755.5" height="60" x="120" y="220"></rect></g></g></g></svg></span> | <span class="math-inline" dir="ltr" style="display:inline-block;direction:ltr;unicode-bidi:isolate;vertical-align:baseline;white-space:nowrap;margin:0 2px;"><svg aria-label="P(n,r)=\frac{n!}{(n-r)!}" data-tex="P(n,r)=\frac{n!}{(n-r)!}" style="display:inline-block;vertical-align: -1.238ex;" xmlns="http://www.w3.org/2000/svg" width="15.471ex" height="3.275ex" role="img" focusable="false" viewBox="0 -900.3 6838.2 1447.4" xmlns:xlink="http://www.w3.org/1999/xlink"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D443" xlink:href="#MJXG-TEX-I-1D443"></use></g><g data-mml-node="mo" transform="translate(751,0)"><use data-c="28" xlink:href="#MJXG-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(1140,0)"><use data-c="1D45B" xlink:href="#MJXG-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(1740,0)"><use data-c="2C" xlink:href="#MJXG-TEX-N-2C"></use></g><g data-mml-node="mi" transform="translate(2184.7,0)"><use data-c="1D45F" xlink:href="#MJXG-TEX-I-1D45F"></use></g><g data-mml-node="mo" transform="translate(2635.7,0)"><use data-c="29" xlink:href="#MJXG-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(3302.4,0)"><use data-c="3D" xlink:href="#MJXG-TEX-N-3D"></use></g><g data-mml-node="mfrac" transform="translate(4358.2,0)"><g data-mml-node="mrow" transform="translate(929.6,394) scale(0.707)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJXG-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(600,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g></g><g data-mml-node="mrow" transform="translate(220,-370.3) scale(0.707)"><g data-mml-node="mo"><use data-c="28" xlink:href="#MJXG-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(389,0)"><use data-c="1D45B" xlink:href="#MJXG-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(989,0)"><use data-c="2212" xlink:href="#MJXG-TEX-N-2212"></use></g><g data-mml-node="mi" transform="translate(1767,0)"><use data-c="1D45F" xlink:href="#MJXG-TEX-I-1D45F"></use></g><g data-mml-node="mo" transform="translate(2218,0)"><use data-c="29" xlink:href="#MJXG-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(2607,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g></g><rect width="2240" height="60" x="120" y="220"></rect></g></g></g></svg></span> |

---

ملخص سريع

- التوافيق تعني **اختيار دون ترتيب**. - إذا كان ترتيب العناصر لا يغير النتيجة، نستخدم **التوافيق**. - قانون التوافيق:

<div class="math-display" style="text-align:center;margin:10px 0;direction:ltr;overflow-x:auto;max-width:100%;"><svg aria-label="C(n,r)=\frac{n!}{r!(n-r)!}" data-tex="C(n,r)=\frac{n!}{r!(n-r)!}" style="display:block;margin:0 auto;vertical-align: -2.172ex;" xmlns="http://www.w3.org/2000/svg" width="20.058ex" height="5.321ex" role="img" focusable="false" viewBox="0 -1392 8865.7 2352" xmlns:xlink="http://www.w3.org/1999/xlink"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math"><g data-mml-node="mi"><use data-c="1D436" xlink:href="#MJXG-TEX-I-1D436"></use></g><g data-mml-node="mo" transform="translate(760,0)"><use data-c="28" xlink:href="#MJXG-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(1149,0)"><use data-c="1D45B" xlink:href="#MJXG-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(1749,0)"><use data-c="2C" xlink:href="#MJXG-TEX-N-2C"></use></g><g data-mml-node="mi" transform="translate(2193.7,0)"><use data-c="1D45F" xlink:href="#MJXG-TEX-I-1D45F"></use></g><g data-mml-node="mo" transform="translate(2644.7,0)"><use data-c="29" xlink:href="#MJXG-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(3311.4,0)"><use data-c="3D" xlink:href="#MJXG-TEX-N-3D"></use></g><g data-mml-node="mfrac" transform="translate(4367.2,0)"><g data-mml-node="mrow" transform="translate(1810.2,676)"><g data-mml-node="mi"><use data-c="1D45B" xlink:href="#MJXG-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(600,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g></g><g data-mml-node="mrow" transform="translate(220,-710)"><g data-mml-node="mi"><use data-c="1D45F" xlink:href="#MJXG-TEX-I-1D45F"></use></g><g data-mml-node="mo" transform="translate(451,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g><g data-mml-node="mo" transform="translate(729,0)"><use data-c="28" xlink:href="#MJXG-TEX-N-28"></use></g><g data-mml-node="mi" transform="translate(1118,0)"><use data-c="1D45B" xlink:href="#MJXG-TEX-I-1D45B"></use></g><g data-mml-node="mo" transform="translate(1940.2,0)"><use data-c="2212" xlink:href="#MJXG-TEX-N-2212"></use></g><g data-mml-node="mi" transform="translate(2940.4,0)"><use data-c="1D45F" xlink:href="#MJXG-TEX-I-1D45F"></use></g><g data-mml-node="mo" transform="translate(3391.4,0)"><use data-c="29" xlink:href="#MJXG-TEX-N-29"></use></g><g data-mml-node="mo" transform="translate(3780.4,0)"><use data-c="21" xlink:href="#MJXG-TEX-N-21"></use></g></g><rect width="4258.4" height="60" x="120" y="220"></rect></g></g></g></svg></div>

- في مثال الدوري بين **5 فرق**، عدد المباريات هو:

**10 مباريات**.