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Sam has 8 trousers and 12 shirts. 2 particular trousers can never be

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Abhijeet007
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Sam has 8 trousers and 12 shirts. 2 particular trousers can never be [#permalink] New post   01 Apr 2019, 05:43
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65% (hard)

Question Stats:

56% (02:17) correct 44% (02:59) wrong based on 48 sessions
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Sam has 8 trousers and 12 shirts. 2 particular trousers can never be worn with any one of 3 particular shirts, and 2 other particular trousers must be worn with any one of 4 other particular shirts. In how many ways can Sam match up a trouser with a shirt?

(A) 94
(B) 88
(C) 66
(D) 82
(E) 74

Source:- EduShastra Class Sheet.
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E
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lucajava
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Sam has 8 trousers and 12 shirts. 2 particular trousers can never be [#permalink] New post   01 Apr 2019, 07:37
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\(2*9 = 18\), where 9 = 12 shirts - 3 particular shirts that can never be worn
\(2*4 = 8\)
\(4*12 = 48\), trousers without dress restrictions.

Sum all cases: \(74\). Hence, E.
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Re: Sam has 8 trousers and 12 shirts. 2 particular trousers can never be [#permalink] New post   02 Apr 2019, 04:15
As two trousers can't be worn by 3 particular shirts, hence they can be worn by rest 9 shirts. Combination possible= 2*9
2 trousers must be worn with 4 particular shirts, combinations possible= 2*4
Rest 4 trouser can be worn with any of the 12 shirts, combination possible=4*12
Total number of combinations=74
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Re: Sam has 8 trousers and 12 shirts. 2 particular trousers can never be [#permalink] New post   03 Apr 2019, 17:59
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Abhijeet007 wrote:
Sam has 8 trousers and 12 shirts. 2 particular trousers can never be worn with any one of 3 particular shirts, and 2 other particular trousers must be worn with any one of 4 other particular shirts. In how many ways can Sam match up a trouser with a shirt?

(A) 94
(B) 88
(C) 66
(D) 82
(E) 74

Source:- EduShastra Class Sheet.



For the 2 particular trousers that can never be worn with any one of 3 particular shirts, each has 9 shirts to pair with, so there are 2 x 9 = 18 pairings.

For the 2 other particular trousers that must be worn with any one of 4 other particular shirts, there are 2 x 4 = 8 pairings.

For the remaining 4 trousers, each has 12 shirts to pair with, so there are 4 x 12 = 48 pairings.

Therefore, the total is 18 + 8 + 48 = 74 pairings.

Answer: E
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gmatclubot
Re: Sam has 8 trousers and 12 shirts. 2 particular trousers can never be [#permalink]
03 Apr 2019, 17:59
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