Math Question Help

Question

1. Q; There are 18 baseball players and 16 basketball players who are running a sports camp. In

how many ways could they form a 4-member fund raising committee if

1. At least two basketball players are selected. (Don't simplify)

Explain please.

Answer 1

There are three possibilities given that at least two basketball players are selected.

1) 2 basketball players are selected and 2 baseball players are selected

2) 3 basketball players are selected and 1 baseball players are selected

3) 4 basketball players are selected and 0 baseball players are selected

For scenario 1)

The number of possible ways of choosing 2 basketball players from a total of 16 is ₁₆C₂

The number of possible ways of choosing 2 baseball players from a total of 18 is ₁₈C₂

Thus the number of ways of choosing 2 basketball players and 2 baseball players is ₁₆C₂ * ₁₈C₂

For scenario 2)

The number of possible ways of choosing 3 basketball players from a total of 16 is ₁₆C₃

The number of possible ways of choosing 1 baseball players from a total of 18 is ₁₈C₁

Thus the number of ways of choosing 3 basketball players and 1 baseball players is ₁₆C₃ * ₁₈C₁

Scenario 3)

Similar to the first two scenarios

The number of ways of choosing 4 basketball players and 0 baseball players is ₁₆C₄ * ₁₈C₀

Add up all these possibilities.