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A septet, a group composed of seven players, is made up of
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08 Oct 2017, 22:44
08 Oct 2017, 22:44
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Question Stats:
83% (00:39) correct
16% (01:53) wrong based on 6 sessions
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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
Kudos for correct solution.
(A) 35
(B) 70
(C) 210
(D) 420
(E) 1225
Kudos for correct solution.
Re: A septet, a group composed of seven players, is made up of
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09 Oct 2017, 02:04
09 Oct 2017, 02:04
1
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
Kudos for correct solution.
(A) 35
(B) 70
(C) 210
(D) 420
(E) 1225
Kudos for correct solution.
Here we need to choose 4 strings out of 7 and 3 woodwind out of 7
i.e 7C4 * 7C3
= 35 * 35 =1225
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Re: A septet, a group composed of seven players, is made up of
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02 Jan 2018, 09:23
02 Jan 2018, 09:23
Expert Reply
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
(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
