Q. If $^{n} C_{12} =^{n} C_{8}$ , then $n$ is equal to

1664 195 Permutations and Combinations Report Error

A

$20$

60%

B

$12$

16%

C

$6$

18%

D

$30$

6%

Solution:

Given, $^{n} C_{12} =^{n} C_{8}$
$∴^{n} C_{n - 2} =^{n} C_{8} (∵^{n} C_{r} =^{n} C_{n - r})$
$\Rightarrow n - 12 = 8$
$\Rightarrow n = 20$