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In how many ways can 5 boys and 3 girls be seated on 8

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In how many ways can 5 boys and 3 girls be seated on 8 [#permalink] New post 24 Sep 2012, 13:02
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Question Stats:

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In how many ways can 5 boys and 3 girls be seated on 8 chairs so that no two girls are together?

A. 5760
B. 14400
C. 480
D. 56
E. 40320

[Reveal] Spoiler:
HEre's what I did :

5! * (4C3) *2* 3! = 120*6*4*2= 5760. Am I correct?
[Reveal] Spoiler: OA

Last edited by voodoochild on 24 Sep 2012, 13:37, edited 1 time in total.
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Re: In how many ways can 5 boys and 3 girls [#permalink] New post 24 Sep 2012, 13:23
voodoochild wrote:
In how many ways can 5 boys and 3 girls be seated on 8 chairs so that no two girls are together?


A 5760
B 14400
C 480
D 56
E 40320

HEre's what I did :

5! * (4C3) *2* 3! = 120*6*4*2= 5760. Am I correct?


Consider the following arrangement:

*B*B*B*B*B*

Now, if girls occupy the places of 6 stars no girls will be together.

# of ways 3 girls can occupy the places of these 6 stars is C^3_6=20;
# of ways 3 girls can be arranged on these places is 3!=6;
# of ways 5 boys can be arranged is 5!=120.

So total # of ways to arrange 3 Girls and 5 boys so that no girls are together is 20*6*120=14,000.

Answer: B.
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Manager
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Re: In how many ways can 5 boys and 3 girls [#permalink] New post 24 Sep 2012, 13:37
Bunuel wrote:
voodoochild wrote:
In how many ways can 5 boys and 3 girls be seated on 8 chairs so that no two girls are together?


A 5760
B 14400
C 480
D 56
E 40320

HEre's what I did :

5! * (4C3) *2* 3! = 120*6*4*2= 5760. Am I correct?


Consider the following arrangement:

*B*B*B*B*B*

Now, if girls occupy the places of 6 stars no girls will be together.

# of ways 3 girls can occupy the places of these 6 stars is C^3_6=20;
# of ways 3 girls can be arranged on these places is 3!=6;
# of ways 5 boys can be arranged is 5!=120.

So total # of ways to arrange 3 Girls and 5 boys so that no girls are together is 20*6*120=14,000.

Answer: B.


Bunuel,

Here's what I thought:

_ O _ O _ O _ O

3 G can occupy any of the 4 "_" positions in 4C3 ways.

Similar Girls could also occupy any of the 4 "O" positions in 4C3 ways.

Boys can be permuted in 5! ways. Girls - 3! Therefore arrangements = 4C3* 2 * 5! * 3! = 4*2*120*6= 5760. Can you please let me know what I am missing?

Thanks
Manager
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Joined: 16 Feb 2011
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Re: In how many ways can 5 boys and 3 girls be seated on 8 [#permalink] New post 24 Sep 2012, 13:59
Please ignore. I got it. 4C3 should be 6C3.

Arrangemnets = 6C3 * 5! * 3! = B...thanks
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Re: In how many ways can 5 boys and 3 girls [#permalink] New post 24 Sep 2012, 14:32
Bunuel wrote:
voodoochild wrote:
In how many ways can 5 boys and 3 girls be seated on 8 chairs so that no two girls are together?


A 5760
B 14400
C 480
D 56
E 40320

HEre's what I did :

5! * (4C3) *2* 3! = 120*6*4*2= 5760. Am I correct?


Consider the following arrangement:

*B*B*B*B*B*

Now, if girls occupy the places of 6 stars no girls will be together.

# of ways 3 girls can occupy the places of these 6 stars is C^3_6=20;
# of ways 3 girls can be arranged on these places is 3!=6;
# of ways 5 boys can be arranged is 5!=120.

So total # of ways to arrange 3 Girls and 5 boys so that no girls are together is 20*6*120=14,000.

Answer: B.


Small typo: 20*6*120=14,000 should be 14,400.
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Re: In how many ways can 5 boys and 3 girls   [#permalink] 24 Sep 2012, 14:32
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