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Permutations and Combinations (p-2) — Maths (commerce) STD 11 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 11 Commerce / ArtsMaths (commerce)Permutations and Combinations (p-2)1 Mark
Question
Find $n$ if ${ }^{23} C_{3 n}={ }^{23} C_{2 n+3}$
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Answer

$
\begin{aligned}
& { }^{23} C_{3 n}={ }^{23} C_{2 n+3} \\
& \text { If }{ }^n C_x={ }^n C_y \text {, then either } x=y \text { or } x=n-y \\
& \therefore 3 n=2 n+3 \text { or } 3 n=23-2 n-3 \\
& \therefore n=3 \text { or } n=4
\end{aligned}
$

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