Combinations

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

This medium difficulty mathematics question is from the chapter permutations and combinations, covering the topic of combinations. It appeared in the 2025 exam.

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Combinations

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