#### Answer

$_{11}$C$_{5}$ is greater

#### Work Step by Step

You have $_{11}$C$_{5}$ and $_{11}$C$_{8}$.Solve to find out which is larger:
A:
$_{11}$C$_{5}$=$\frac{11!}{5!(11-5)!}$ -simplify like terms-
$_{11}$C$_{5}$=$\frac{11!}{5! (6!)}$ -write using factorial-
$_{11}$C$_{5}$=$\frac{11*10*9*8*7*6*5*4*3*2*1}{(5*4*3*2*1)(6*5*4*3*2*1)}$ -simplify-
$_{11}$C$_{5}$=462
B:
$_{11}$C$_{8}$=$\frac{11!}{8!(11-8)!}$ -simplify like terms-
$_{11}$C$_{8}$=$\frac{11!}{8! (3!)}$ -write using factorial-
$_{11}$C$_{8}$=$\frac{11*10*9*8*7*6*5*4*3*2*1}{(8*7*6*5*4*3*2*1)(3*2*1)}$ -simplify-
$_{11}$C$_{8}$=165
$_{11}$C$_{5}$ is greater