Question

In how many ways can a cricket team of $11$ players selected out of $16$ players if two particular players are to be included and one particular player is to be rejected ?

• A. $715$
• B. $615$
• C. $915$
• D. $515$

Answer 1

The correct option is A $715$

$11$ players can be selected out of $16$ in ${}^{16}{C}_{11}$ ways $=\frac{16!}{11!\times 5!}=4368$ ways.

Now, if two particular players is to be included and one particular player is to be rejected, then we have to select $9$ more players out of $13$ in ${}^{13}{C}_9$ ways
$=\frac{13!}{9!4!}=715$ ways.