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Carla is having a dinner party and is inviting 5 guests: 3 boys and 2

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Carla is having a dinner party and is inviting 5 guests: 3 boys and 2  [#permalink]

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New post 15 May 2019, 22:54
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Question Stats:

67% (01:42) correct 33% (02:00) wrong based on 48 sessions

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Carla is having a dinner party and is inviting 5 guests: 3 boys and 2 girls. Carla knows that she needs to sit at the head of the table, but hasn't decided on fixed seats for anyone else. If she decides not to sit any of her guests next to anyone else of the same gender, how many different seating arrangements are possible?

A. 6
B. 12
C. 24
D. 36
E. 60

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Re: Carla is having a dinner party and is inviting 5 guests: 3 boys and 2  [#permalink]

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New post 15 May 2019, 23:54
Boys will sit on 2 chairs next to Carla and on 1 chair in the middle of 2 girls. And on the remaining 2 chairs girls will sit
Total sitting arrangements possible= 3!*2!=12
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Re: Carla is having a dinner party and is inviting 5 guests: 3 boys and 2  [#permalink]

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New post 16 May 2019, 01:29
Bunuel wrote:
Carla is having a dinner party and is inviting 5 guests: 3 boys and 2 girls. Carla knows that she needs to sit at the head of the table, but hasn't decided on fixed seats for anyone else. If she decides not to sit any of her guests next to anyone else of the same gender, how many different seating arrangements are possible?

A. 6
B. 12
C. 24
D. 36
E. 60


since head position has to be fixed so there can be only 1 possible way of arrangement
bgbgcg ; 2*3*1*2*1*1 ; 12
IMO B
had it been given that head seat can be moved around ; then we would have to make cases and solve for different combinations ..
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Re: Carla is having a dinner party and is inviting 5 guests: 3 boys and 2  [#permalink]

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New post 16 May 2019, 06:58
There are 2 heads of a 6 chair dining table.
Answer should be 24.
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Carla is having a dinner party and is inviting 5 guests: 3 boys and 2  [#permalink]

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New post 16 May 2019, 09:41
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Bunuel wrote:
Carla is having a dinner party and is inviting 5 guests: 3 boys and 2 girls. Carla knows that she needs to sit at the head of the table, but hasn't decided on fixed seats for anyone else. If she decides not to sit any of her guests next to anyone else of the same gender, how many different seating arrangements are possible?

A. 6
B. 12
C. 24
D. 36
E. 60



Possible seating arrangement:

------------_C_
---------_B_ _B_
---------_G_ _G_
-------------_B_

Each boy can seat in any of the 3 chairs= 3!
Each girl can seat in any of the 2 chairs= 2!

Possible combination= 3! * 2! = 12

Option B
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Re: Carla is having a dinner party and is inviting 5 guests: 3 boys and 2  [#permalink]

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New post 19 May 2019, 19:25
Bunuel wrote:
Carla is having a dinner party and is inviting 5 guests: 3 boys and 2 girls. Carla knows that she needs to sit at the head of the table, but hasn't decided on fixed seats for anyone else. If she decides not to sit any of her guests next to anyone else of the same gender, how many different seating arrangements are possible?

A. 6
B. 12
C. 24
D. 36
E. 60



The arrangements must be:

B - G - B - G - B

She can seat any of 3 boys in the first position, either of 2 girls in the second position, any of the remaining 2 boys in the third position, the single remaining girl in the fourth position, and the single remaining boy in the fifth position. Thus, the number of arrangements is 3 x 2 x 2 x 1 x 1 = 12.

Answer: B
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Re: Carla is having a dinner party and is inviting 5 guests: 3 boys and 2  [#permalink]

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New post 21 May 2019, 20:47
Dont assume until its mentioned in the question.

Sneha333 wrote:
There are 2 heads of a 6 chair dining table.
Answer should be 24.

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Re: Carla is having a dinner party and is inviting 5 guests: 3 boys and 2   [#permalink] 21 May 2019, 20:47
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