If $^{n} C_{3} =^{n} C_{2},$ then n is equal to

2

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3

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5

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None of these

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Solution

The correct option is C $5$
Given,
$^{n} C_{3} =^{n} C_{2}$
$\frac{n!}{3! (n - 3)!} = \frac{n!}{2! (n - 2)!}$
$\frac{n!}{3 \times 2! (n - 3)!} = \frac{n!}{2! (n - 2) (n - 3)!}$
$\frac{1}{3} = \frac{1}{(n - 2)}$
$n - 2 = 3$
$n = 5$

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x

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