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A promoter is organizing an opera concert. Ten singers are a

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A promoter is organizing an opera concert. Ten singers are a [#permalink] New post 27 Aug 2018, 13:57
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A promoter is organizing an opera concert. Ten singers are available for the program: 3 sopranos, 3 mezzos, 2 tenors and 2 baritones. If the promoter intends every segment to be a duet by performers with different vocal ranges, how many pairings of performers are possible?


A. 6

B. 10

C. 24

D. 36

E. 37
[Reveal] Spoiler: OA

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Re: A promoter is organizing an opera concert. Ten singers are a [#permalink] New post 28 Aug 2018, 06:39
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A promoter is organizing an opera concert. Ten singers are available for the program: 3 sopranos, 3 mezzos, 2 tenors and 2 baritones. If the promoter intends every segment to be a duet by performers with different vocal ranges, how many pairings of performers are possible?


The solution here is to find number of combination by organizing each pair of singers to other.

1. So we have groups of 3M 3S 2T 2B

2. Lets pair them

M S = 3C1 * 3C1 = 9
M T = 3C1 * 2C1 = 6
M B = 3C1 * 2C1 = 6
S T = 3C1 * 2C1 = 6
S B = 3C1 * 2C1 = 6
T B = 2C1 * 2C1 = 4


Total = 37

answer is E
Re: A promoter is organizing an opera concert. Ten singers are a   [#permalink] 28 Aug 2018, 06:39
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A promoter is organizing an opera concert. Ten singers are a

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