A cricket team of 11 players is to be chosen from 15 players, but one particular player must be included. In how many ways can the team be chosen?

Introduction / Context:A mandatory selection reduces the degrees of freedom by fixing one seat. We then choose the remaining players from the rest.

Given Data / Assumptions:

• Total players = 15.
• Team size = 11.
• One particular player is always selected.

Concept / Approach:If one player is fixed, we need to choose 10 more from the remaining 14. The number of such teams is C(14,10).

Step-by-Step Solution:C(14,10) = C(14,4) (by symmetry) = 1001.

Verification / Alternative check:Compute directly: 14*13*12*11 / (4*3*2*1) = 24024 / 24 = 1001.

Why Other Options Are Wrong:Other values correspond to choosing 11 from 15 without the mandatory constraint or arithmetic slips.

Common Pitfalls:Subtracting the mandatory player from total team size incorrectly (e.g., recalculating as C(15,11)).

Final Answer:1001