BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
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

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1