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Binomial Theorem — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsBinomial Theorem3 Marks
Question
If $^nC_{10} =\ ^nC_{12},$ Find $^{23}C_n.$
✓

Answer

We have,
If $^nC_p =\ ^nC_q = n$
Then $p + q = n$
Also,
$\Rightarrow\ ^nC_{10} =\ ^nC_{12}$
$10 + 12 = n$
$\Rightarrow n = 22$
Applying (i),
${^\text{23}}\text{C}_{\text{22}}=\frac{\text{23!}}{22!1!}$
$=\frac{23\times22!}{22!}$
$=23$

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