Question

For the cricket world cup, playing 11 is to be selected out of 16 players in the squad. In how many ways can this be done?

• A. $\frac{16!}{5!\times 11!}$
• B. $\frac{16!}{11!}$
• C. $\frac{16!}{5!}$
• D. None of the above

Answer 1

The correct option is A $\frac{16!}{5!\times 11!}$

We know that number of ways of selecting "r" things out of "n" things at a time is equal to ${}^n{C}_r=\frac{n!}{(n-r)!.r!}.$

In the above question $11$ players are to be selected out of $16$ for the playing $11.$

So, the number of ways of doing that is equal to ${}^{16}{C}_{11}$
$\Rightarrow {}^{16}{C}_{11}=\frac{16!}{(16-11)!\times 11!}$

$\Rightarrow {}^{16}{C}_{11}=\frac{16!}{5!\times 11!}$