Q. If $^{n} C_{9} =^{n} C_{8}$ , find $^{n} C_{17}$ .

2152 279 Permutations and Combinations Report Error

A

$1$

71%

B

$2$

9%

C

$0$

13%

D

$3$

6%

Solution:

$^{n} C_{p} =^{n} C_{k}$
$\Rightarrow n = p + k$
$∴^{n} C_{9} =^{n} C_{8}$
$\Rightarrow n = 9 + 8 = 17$
Now $^{17} C_{17} = 1$