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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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).
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).
Rahul Lakhani
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Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
