Barbara has 8 shirts and 9 pants. How many clothing combinat

[BTGmoderatorAT]

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?

[EconomistGMATTutor]

Hello ardz24. I am going to give you an explanation here.

The total number of clothing combinations Barbara has with 8 shirts and 9 pants is 8*9=72.

But, we have the condition: she doesn't wear 2 specific shirts with 3 specific pants. We get two cases:

- When she uses any of this 2 shirts, she only can use 6 pants, so she has 2*6=12 possible clothing combinations.

- When she uses the any of the other 6 shirts, she has 9 pants to choose. So the clothing combinations in this case is 6*9=54.

Finally, the total of clothing combinations Barbara has is 12+54=66.

The correct answer is B.

I really hope it helps you.

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Hi ardz24,

With 8 shirts and 9 pants, if there were no restrictions, then there would be (8)(9) = 72 possible outfits. However, we're told that 2 of the shirts will not be worn with 3 of pants. This means that (2)(3) = 6 of the possible combinations will NOT be available. Thus, the total number of combinations is...

72 - 6 = 66

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

[Matt@VeritasPrep]

We could also compile the valid combinations as follows.

6 shirts can go with any pants: 6 * 9
2 shirts can go with exactly 6 pants: 2 * 6

6 * 9 + 2 * 6 => 66

[BTGmoderatorAT]

Thank you Matt for your clear explanation

[Scott@TargetTestPrep]

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