Combinations

Question

The number of ways to select a cricket team of 11 players from 15 players, where 2 particular players must be included, is

RankGuru · Accepted Answer

1. **Analyze Constraints**: We need a team of 11. 2 players are *already selected* (mandatory inclusion).
2. **Selection Task**: We need to pick the remaining $11 - 2 = 9$ players.
3. **Available Pool**: We pick these from the remaining $15 - 2 = 13$ players.
4. **Apply Combination**: $\binom{13}{9}$.
5. **Symmetry Property**: $\binom{13}{9} = \binom{13}{4}$.
6. **Calculation**:
   - $\binom{13}{4} = \frac{13 	imes 12 	imes 11 	imes 10}{4 	imes 3 	imes 2 	imes 1} = \frac{13 	imes 11 	imes 10}{2} = 13 	imes 11 	imes 5 = 715$.
7. **Result**: 715 ways.

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