Question

The number of ways in which a team of $11$ players can be selected from $22$ players including $2$ of them and excluding $4$ of them is.

• A. ${}^1{}^6{C}_6$
• B. ${}^1{}^6{C}_7$
• C. ${}^1{}^6{C}_8$
• D. ${}^2{}^0{C}_7$

Answer 1

Answer: (B)

${}^1{}^6{C}_7$

Here we have total $22$ players out of which we have to select 11, but it is given that $4$ out of $22$ to be excluded from selection so we have to select $11$ from rest $18$.
Again it said that $2$ out of $18$ has to be included in the squad, so we are left with $9$ selection out of remaining $16$ players.
Hence, required number of ways ${=}^{16}{C}_9{=}^{16}{C}_7$