BTGmoderatorAT wrote:Barbara has 8 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn't wear 2 specific shirts with 3 specific pants?
A. 41
B. 66
C. 36
D. 70
E. 56
Is there a strategic approach to this question?
If we exclude the 2 specific shirts and 3 specific pants that she won't wear together as an outfit, there are 6 x 6 = 36 possible outfits.
If we exclude the 2 specific shirts, then any of the remaining 6 shirts can pair with the 3 specific pants. So there are 6 x 3 = 18 such outfits.
If we exclude the 3 specific pants, then any of the remaining 6 pants can pair with the 2 specific shirts. So there are 6 x 2 = 12 such outfits.
Therefore, there are a total of 36 + 18 + 12 = 66 possible outfits.
Alternate Solution:
Without any restrictions, she has 8 x 9 = 72 possible outfits. We are told that Barbara does not wear 2 specific shirts with 3 specific pants; thus, of the 72 total outfits, 2 x 3 = 6 of them are never worn. So, the number of possible outfits is 72 - 6 = 66.
Answer: B
