In how many different ways can these 3 tasks be assigned?

Question

Part A:

A committee has 7 members. 3 different members are needed for 3 special tasks: one member will promote plastic recycling, one member will promote glass recycling, and one member will promote paper recycling. In how many different ways can these 3 tasks be assigned?

Part B: if the committee consists of 3 males and 4 females, in how many ways can the tasks be assigned so that both males and females are given tasks?

Answer 1

(a) The plastic can be chosen in 7 ways, the recycling then in 6, and the paper then in 5, so 7 x 6 x 5 = 210 ways

(b) Number of ways that the tasks can be assigned = 210 from (a)

In how many of these are both males and females given tasks?

Suppose we have only males or only females

If only males we can fill the tasks in 3 x 2 x 1 = 6 ways

Only females we can fill the tasks in 4 x 3 x 2 = 24 ways

So if both males and females are given tasks number of ways = 210 - 6 - 24 = 180