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# A promoter is organizing an opera concert. Ten singers are available f

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Board of Directors
Joined: 01 Sep 2010
Posts: 3405
A promoter is organizing an opera concert. Ten singers are available f  [#permalink]

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27 Aug 2018, 14:58
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Difficulty:

55% (hard)

Question Stats:

59% (02:18) correct 41% (02:16) wrong based on 46 sessions

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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

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Joined: 02 Aug 2009
Posts: 7996
Re: A promoter is organizing an opera concert. Ten singers are available f  [#permalink]

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27 Aug 2018, 20:18
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carcass wrote:
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

So we have to choose two performers , each from a different group..

Let's see ways ..
1) S and M - 3*3=9
2) S and T - 3*2=6
3) S and B - 3*2=6
4) M and T - 3*2=6
5) M and B - 3*2=6
6) T and B - 2*2=4

Total - 9+6+6+6+6+4 = 37

E

Another give away are the choices..
In the numbers only 3*3 will be odd ways, when S and M and rest all will be even as T and B are even so our answer has to be ODD as O+E+E+E....=O

E
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Joined: 13 Mar 2019
Posts: 3
GMAT 1: 690 Q42 V41
A promoter is organizing an opera concert. Ten singers are available f  [#permalink]

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09 Jun 2019, 03:59
1
Another way to go about this is to say there are 10c2 ways to find pairs of singers.

To find the ways we can create duets without them being in the same vocal range is 10c2-3c2 (i.e. Sopranos) - 3c2 (i.e. Mezzos) - 2c2 (i.e. Tenors) - 2c2 (i.e. Baritones) = 45-3-3-1-1 = 37
A promoter is organizing an opera concert. Ten singers are available f   [#permalink] 09 Jun 2019, 03:59
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