Question

A team of 11 cricket players is to be chosen from 15 players. In how many ways can this be done so as to:

1. Include a particular player A.

2. Exclude a particular player B.

3. Include A and exclude B.

Answer 1

1. A particular player A is to be included, then selection of 10 is to be made from 14 players.

The required number of ways 14C₁₀ = 14C₄ = \(\frac{14 \times 13 \times 12 \times 11}{1 \times 2 \times 3 \times 4}\)  = 7 × 13 × 11 = 1001.

2. A particular player B is to be excluded, then selection of 11 is to be made from 14 players.

The required number of ways = 14C₁₁ = 14C₃ = \(\frac{14 \times 13 \times 12}{1 \times 2 \times 3}\)

= 14 × 13 × 2 = 364.

3. A particular player A is to be included and player B is to be excluded, then selection of 10 is to be made from 13 players. The required number of ways

= 13C₁₀ = 13C₃ = \(\frac{13 \times 12 \times 11}{1 \times 2 \times 3}\)

= 13 × 2 × 11 = 286.