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

The correct option is C

${}^{12}C_4$

Explanation for the Correct Option:

Finding the number of ways to form a team:

Total number of players = $22$

We are supposed to create a team of $10$ players.

Out of the $22$ players, $4$ players will always be excluded.

This means we are left with only $18$ players to select from.

Now, out of these $18$ players, $6$ players will always be included.

This means that we are left with $12$ players only to form a team of $4$.

Therefore, the required number of ways is: ${}^{12}C_4$

Hence, Option (C) is correct.