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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

tricky counting - Four women and three men must be seated

by Brent@GMATPrepNow » Wed Apr 19, 2017 5:18 am

Four women and three men must be seated in a row for a group photograph. If no two men can sit next to each other, in how many different ways can the seven people be seated?

A) 240
B) 480
C) 720
D) 1440
E) 5640

Answer: D

Source: www.gmatprepnow.com
Difficulty level: 700

Last edited by Brent@GMATPrepNow on Wed Apr 19, 2017 6:20 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Wed Apr 19, 2017 5:18 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Wed Apr 19, 2017 6:16 am

Brent@GMATPrepNow wrote:Four women and three men must be seated in a row for a group photograph. If no two men can sit next to each other, in how many different ways can the seven people be seated?

A) 240
B) 480
C) 720
D) 4880
E) 5640

Number of ways to arrange the four women = 4! = 24.

Once the 4 women have been arranged, the 3 men must be kept separated.
Thus, the 3 men may occupy any of the 5 empty slots below:
_W_W_W_W_

Number of options for the first man = 5. (Any of the 5 empty slots.)
Number of options for the second man = 4. (Any of the 4 remaining empty slots.)
Number of options for the third man = 3. (Any of the 3 remaining empty slots.)

To combine the options in blue, we multiply:
24*5*4*3 = 1440.

The correct answer is D.

Last edited by GMATGuruNY on Wed Apr 19, 2017 6:24 am, edited 1 time in total.

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Wed Apr 19, 2017 6:21 am

GMATGuruNY wrote:
Number of ways to arrange the four women = 4! = 24.

Once the 4 women have been arranged, the 3 men may occupy any of the 5 empty slots below:
_W_W_W_W_

Number of options for the first man = 5. (Any of the 5 empty slots.)
Number of options for the second man = 4. (Any of the 4 remaining empty slots.)
Number of options for the third man = 3. (Any of the 3 remaining empty slots.)

To combine the options in blue, we multiply:
24*5*4*3 = 1440.

The correct answer does not seem to be among the answer choices.