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
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tricky counting - Four women and three men must be seated
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Last edited by Brent@GMATPrepNow on Wed Apr 19, 2017 6:20 am, edited 1 time in total.
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Number of ways to arrange the four women = 4! = 24.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
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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Brent@GMATPrepNow
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Good catch!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.
I've edited the answer choices.
Cheers,
Brent
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