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

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Intern
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Joined: 20 Jan 2018
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Location: India
Concentration: Operations, International Business
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Sam has 8 trousers and 12 shirts. 2 particular trousers can never be  [#permalink]

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New post 01 Apr 2019, 04:43
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A
B
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D
E

Difficulty:

  55% (hard)

Question Stats:

58% (02:09) correct 42% (03:00) wrong based on 36 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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Joined: 21 Feb 2019
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Sam has 8 trousers and 12 shirts. 2 particular trousers can never be  [#permalink]

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New post 01 Apr 2019, 06:37
2
\(2*9 = 18\), 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]

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New post 02 Apr 2019, 03:15
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]

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New post 03 Apr 2019, 16:59
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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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Re: Sam has 8 trousers and 12 shirts. 2 particular trousers can never be   [#permalink] 03 Apr 2019, 16:59

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

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