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There are 15 possibilities. In psuedo-code, the math works out like this: n = 42-1 where n is the number of possibilities, 4 is the size of a quartette, 2 is the number of different types of singers, and -1 reflects that a quartet of all non-sopranos does not meet your criteria.

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15y ago
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2d ago

The number of ways the director can choose a quartet with at least one soprano is the total number of ways minus the number of ways with no sopranos. Thus, the director can choose a quartet with at least one soprano in (1 - \frac{\binom{8}{4}}{\binom{14}{4}}) ways.

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Q: How many ways can the director choose a quartet that contains at least one sopano if the chorus has six sopranos and eight baritones.?
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