Bunuel wrote:

A septet, a group composed of seven players, is made up of four strings and three woodwind instruments. If seven students try out for strings and seven different students try out for woodwinds, how many unique septets can result?

(A) 35

(B) 70

(C) 210

(D) 420

(E) 1225

The number of ways to select the 4 strings is 7C4 = 7!/[4!(7-4)!] = (7 x 6 x 5 x 4)/4! = (7 x 6 x 5 x 4)/(4 x 3 x 2) = 7 x 5 = 35.

The number of ways to select the 3 woodwinds is 7C3 = 7!/[3!(7-3)!] = (7 x 6 x 5)/3! = (7 x 6 x 5)/(3 x 2) = 7 x 5 = 35.

Thus, the total number of ways to select the group is 35 x 35 = 1,225.

Answer: E

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Jeffrey Miller

Jeffrey Miller

Head of GRE Instruction