In how many ways a team of 10 players out of 22 can be made if 6 particular players are always to be

Question

In how many ways a team of 10 players out of 22 can be made if 6 particular players are always to be included and 4 particular players are always to be excluded ?

Professor PC Thomas Classes · Answer

We need to select $10-6 = 4$ players out of $22 - 6 (	ext{included}) - 4 (	ext{excluded}) = 12$ players. Number of ways = ${ }^{12} C_4 = 495$.