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.
• B.
• C.
• D.

Answer 1

The correct option is C

First from 22 players, we take out 4 particular players, who are excluded always.

Now, total numbers of players in consideration are 22-4 = 18.

We need to select 10 players out of these 18 players. As it is given that 6 particular players are always included, we don't have any flexibility over these 6 players. So, number of players available for selection = 18-6= 12. Out of 10 vacancies, 6 are already filled and 4 vacancies are left.

So, from 12 players, 4 players can be selected in ${}^{12}{C}_4$ ways.