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A septet, a group composed of seven players, is made up of four strings and three woodwind instruments. If seven student

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by Vincen » Wed Jul 22, 2020 12:35 pm

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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

[spoiler]OA=E[/spoiler]

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Re: A septet, a group composed of seven players, is made up of four strings and three woodwind instruments. If seven stu

by Scott@TargetTestPrep » Sat Jul 25, 2020 2:18 pm
Vincen wrote: ↑
Wed Jul 22, 2020 12:35 pm
 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

[spoiler]OA=E[/spoiler]

Solution:

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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