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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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

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

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]

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Wed Jul 22, 2020 12:35 pm

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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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