BTGmoderatorDC wrote: ↑

Sun Oct 16, 2022 7:41 pm

Before leaving for his business trip, Chad asks his assistant to choose and pack four shirts from his closet, which currently contains eight shirts. If each shirt is a different color, including one blue shirt and one pink shirt, and the assistant chooses the shirts at random, what is the probability that the pink shirt will be one of the four packed but the blue shirt will not?

A 4/7
B 1/2
C 27/70
D 2/7
E 9/35


OA D

Source: Veritas Prep

Solution:

The number of ways to select the pink shirt but not blue shirt is 1C1 x 1C0 x 6C3 = (6 x 5 x 4)/3! = 20. (Notice that 1C1 is for the pink shirt to be selected, 1C0 is for the blue shirt not to be selected, and 6C3 is the number of ways to select the 3 shirts from the remaining 6 shirts.)

The number of ways to select 4 shirts from 8 shirts is:
8C4 = 8!/(4! x 4!) = (8 x 7 x 6 x 5)/4! = (8 x 7 x 6 x 5)/(4 x 3 x 2) = 7 x 2 x 5 = 70

Thus, the probability that the pink shirt will be one of the four packed but the blue shirt will not is 20/70 = 2/7.

Answer: D