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

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Carla is having a dinner party and is inviting 5 guests: 3 b [#permalink] New post 01 Aug 2018, 10:31
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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
[Reveal] Spoiler: OA

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Re: Carla is having a dinner party and is inviting 5 guests: 3 b [#permalink] New post 01 Aug 2018, 12:04
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Carcass 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 Carla sit at the head and she decide none of the guest sit next to the same gender so after Carla,

1st seat is taken by a boy and since the no. of boys is 3, so it can be filled up in = 3 ways

2nd seat is taken by a girl and since the no. of girl is 2, so it is filled up in = 2ways

3rd seat is filled by a boy in = 2 ways (As only 2 boys are remaining after filling up the first seat)

4th seat is filled up by a girl in = 1 way (As only 1 girl is remaining after filling up the second seat)

5th seat is filled up by a boy in = 1 way (As only 1 boy is remaining after filling up the first and third seat)

So the total no. of ways the guest can be seated = 3 * 2 * 2 * 1 * 1 = 12 ways
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Re: Carla is having a dinner party and is inviting 5 guests: 3 b [#permalink] New post 07 May 2019, 23:43
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Carcass 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 the number of guests = 5, let take that as 'n'

Now
Number of permutation taking r things can be arranged in \((n-1)! * \frac{1}{2}\)

= \(\frac{{(5 -1)!}}{2}\)

= \(\frac{24}{2} = 12\)
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Re: Carla is having a dinner party and is inviting 5 guests: 3 b   [#permalink] 07 May 2019, 23:43
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Carla is having a dinner party and is inviting 5 guests: 3 b

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