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Opera Singers

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Opera Singers

by pkw209 » Fri Apr 30, 2010 12:33 pm
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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by Rahul@gurome » Fri Apr 30, 2010 8:05 pm
3 sopranos and 3 mezzos can be chosen in 3 × 3 = 9 ways
3 sopranos and 2 tenors can be chosen in 3 × 2 = 6 ways
3 sopranos and 2 baritones can be chosen in 3 × 2 = 6 ways
3 mezzos and 2 tenors can be chosen in 3 × 2 = 6 ways
3 mezzos and 2 baritones can be chosen in 3 × 2 = 6 ways
2 tenors and 2 baritones can be chosen in 2 × 2 = 4 ways
Hence, the required number of pairings of performers = 9 + 6 + 6 + 6 + 6 + 4 = 37

The correct answer is (E).
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