Assume that the committee consists of 6 Republicans and 5 Democrats. A subcommittee of 4 is randomly selected from all subcommittees of 4 which contain at least

Question

What is the probability that the new subcommittee will contain at least 2 Democrats?

Answer 1

The total number of committees is 11 P 4 = 11x10x9x8 = 7920. There are 6 P 4 = 6x5x4x3 = 360 committees with no democrats and 6 P 3 x 5 P 1 x 4 C 3 = 6x5x4x5x4 = 2400 committed with one Democrat. The total number of possible committees with no or one democrat is 2760. The probability of this event is 2760/7920. The complementary probability, which is what you want is 1 - 2760/7920.

 

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