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The answer is 63, show steps
23. The director of a play has found five flute solos, two guitar pieces, and three violin pieces that would work as background music for some of the scenes. There has to be some violin music because it is mentioned in the play. In how many ways can the director choose the three pieces of music for the play?
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Answer #1

The director can chose one, two, or three violin pieces. One violin piece: There are C(3, 1) ways to choose the violin piece and C(7, 2) ways to choose the remaining two pieces. So, the number of combinations with one violin piece is C(3, 1) x C(7, 2) 63. Two violin pieces: The number of combinations is C(3, 2) x C(7, 1) 21 Three violin pieces: There is only one possible choice since only three violin pieces are being considered. Therefore, the total number of possible combinations is 63211 85.

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