A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. if 7 freshmen, 9 sophomores, 7 juniors, and 8 seniors are eligible to be on the committee, in how many ways can the committee be chosen?
2 out of 6 freshmen 3 out of 7 sophomores 4 out of 7 juniors 5 out of 8 seniors
the number of ways you can get 2 out of 6 freshmen is c(6,2) = 15 the number of ways you can get 3 out of 7 sophomores is c(7,3) = 35 the number of ways you can get 4 out of 7 juniors is c(7,4) = 35 the number of ways you can get 5 out of 8 seniors is c(8,5) = 56
the total number of ways you can get 2 freshmen and 3 sophomores and 4 juniors and 5 seniors is therefore 15 * 35 * 35 * 56 = 1,029,000.
