A school is asked to send a delegation of six pupils selected from six badminton players, six tennis players and five squash players. No pupil plays more than one game. The delegation is to consist of at least one, and not more than three, players drawn from each game. Find the number of ways in which the delegation can be selected.
I use the following approach, but I failed to get the correct answer.
Split the problem into seven cases:
(number of badminton players) + (number of tennis players) + (number of squash players) 1 + 2 + 3 1 + 3 + 2 2 + 1 + 3 2 + 2 + 2 2 + 3 + 1 3 + 1 + 2 3 + 2 + 1
Find the number of possible selections for each case. Add the answers, gives 10350.
But the correct answer is 9450.