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Combinations — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSCombinations3 Marks
Question
If nC10 = nC12, Find 23Cn.
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Answer

We have,
If nCp = nCq = n
Then p + q = n
Also,
⇒ nC10 = nC12
10 + 12 = n
⇒ n = 22
Applying (i),
${^\text{23}}\text{C}_{\text{22}}=\frac{\text{23!}}{22!1!}$
$=\frac{23\times22!}{22!}$
$=23$

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