Question

In how many ways a team of $10$ players out of $22$ players can be made if $6$ particular players are always to be included and $4$ particular players are always excluded

• A. ${}^{22}{C}_{10}$
• B. ${}^{18}{C}_3$
• C. ${}^{12}{C}_4$
• D. ${}^{18}{C}_4$

Answer 1

Answer: (C)

${}^{12}{C}_4$

Total number of players$=22$

We have to select a team of $10$ players.

We have to exclude $4$ particulars of them, so only $18$ players are now available.

Also from these $6$ particulars will always be include.

Therefore, we have to select $4$ more players from the remaining $12$ players.

So, the required number of ways$={}^{12}{C}_4$