Question

If ${}^n{P}_4$ = 24,${}^n{C}_5$, then the value of n is

• A. 10
• B. 15
• C. 9
• D. 12

Answer 1

The correct option is C

9

Given, ${}^n{P}_4$ = 24. ${}^n{C}_5$

Therefore, $n(n-1)(n-2)(n-3)$

= $24\times \frac{n(n-1)(n-2)(n-3)(n-4)}{\mathrm{5.4.3.2.1}}$

$\Rightarrow 1$ = $\frac{(n-4)}{5}\Rightarrow n-4$=$5\Rightarrow n$ = 9