Question

In how many ways a team of 11 players can be selected from 15 players if-

• A. $14C11,14C11$
• B. $15C10,15C11$
• C. $14C10,15C11$
• D. $14C10,14C11$

Answer 1

The correct option is D $14C10,14C11$

Case 1: Captain is included.
Here, we have already selected 1 player. Remaining players to be selected are 10 and Total player remaining are 14. So, we have to select 10 players out of 14 players. Selection can be made in $14C10$ ways.

Case 2: captain is not included.
Here, as captain can not be included, we have to select 11 players from 14 players. Selection can be made in $14C11$ ways.