Question

The number of ways in which a team of eleven players can be selected from 22 players, always including 2 of them and excluding 4 of them is

• A. ${}^{16}{C}_{11}$
• B. ${}^{16}{C}_7$
• C. ${}^{16}{C}_9$
• D. ${}^{20}{C}_9$

Answer 1

Answer: (B), (C)

${}^{16}{C}_7$
${}^{16}{C}_9$

$11$ players are to be selected

out of $22$

$2$ are included

$4$ are excluded

$=9$ are to be selected out of $16$

=${}^{16}{C}_9$

${}^n{C}_r{=}^n{C}_{n-r}{}^{}{}^{16}{C}_9{=}^{16}{C}_7$