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

8 shirts
9 pants

we can combine 2 shirts with (9-3) pants
2*6=12

we can combine the other shirts (6) with any pants (9)
6*9=54

Thus total :12+54=66

I have understood the above approaches . However, would like folks to answer that what is wrong with the below approach.

9 pants - 3 specific avoided - 6 pants
8 shirts - 2 specific avoided - 6 shirts

6C1 * 6C1 = 36 (select one from each for a combination)

What is wrong ?

Rgds,
TGC !

hi TGC,

Question is: 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?

it means he is going to wear all pants and shirts except few combinations he is going to avoid.
so there are 2 groups now
6 shirts ==>they all have choices of 9 pants therefore total ways = \(6C1*9C1 = 54\)
NOW the left 2 shirts is going to avoid 3 pants therefore we have 6 pants hence total ways = \(2C1*6C1 =12\)

hence total choice = \(54 +12 =66\)

what you are doing is that you are just removing those shirts and pants.

hope it helps

I think you didn't get my question.

My question is that what is wrong in my method?

Rgds,
TGC !

You are interpreting question in wrong way.

let say there are 9 pants numbered :1 2 3 4 5 6 7 8 9
AND 8 shirts numbered : 10 11 12 13 14 15 16 17

now question is saying you cannot wear pants numbered : 1, 2, 3 with shirt 10 and 11
but this doesnt mean that you cannot wear pants numbered : 1, 2, 3 with shirt 12 13 14 15 16 17 ===>you are missing this case.

what you are doing is that you are just removing pants 1,2,3 and shirts 10,11.
thats why you are having 6 shirts and 6 pants.

hope this now makes sense.

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

The right answer is B.66 clothing combinat

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