Problem: a department of 10 people - 6 men and 4 women - needs to send a team of 5 to a conference . if they want to make sure that there are no more than 3 members of the team from any one gender , how many distinct groups are possible to send ?
Rationale: they can make a team of 3 men and 2 women . the number of ways to do this is 6 c 3 * 4 c 2 = 20 * 6 = 120 they can make a team of 2 men and 3 women . the number of ways to do this is 6 c 2 * 4 c 3 = 15 * 4 = 60 the total number of distinct groups is 180 . the answer is c .
annotated_formula: add(add(multiply(multiply(6, 5), 4), multiply(6, 5)), multiply(6, 5))