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

2070 239 Permutations and Combinations Report Error

A

$1$

72%

B

$2$

10%

C

$0$

12%

D

$3$

7%

Solution:

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