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?

37

Step-by-step explanation:

Since it is a duet performance we have to pair each singing group to another with all the possible groupings available.

The groups available are

3Mezzos

3Sorprano

2Tenor

2Barritones

Pairing them together we have

Mezzos and Sorprano = 3 * 3 = 9

Mezzos and Tenor = 3 * 2 = 6

Mezzos and Barritone = 3 * 2 = 6

Sorprano and Ternor = 3 * 2 = 6

Sorprano and Barritone = 3 * 2 = 6

Ternor and Barritone = 2 * 2 = 4

Total = 37.