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In how many different ways can 3 boys and 3 girls be seated in a row

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In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

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New post 04 Jan 2017, 01:04
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In how many different ways can 3 boys and 3 girls be seated in a row of 6 chairs such that the girls are not separated, and the boys are not separated?

A. 24
B. 36
C. 72
D. 144
E. 288

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Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

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New post 04 Jan 2017, 01:12
3!*3!*2! = 6*6*2 = 72

Answer C
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Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

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New post 04 Jan 2017, 02:32
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Bunuel wrote:
In how many different ways can 3 boys and 3 girls be seated in a row of 6 chairs such that the girls are not separated, and the boys are not separated?

A. 24
B. 36
C. 72
D. 144
E. 288


Lets consider the group of all boys as one entity and group of girls as other entity

Now we have two entities to arrange which is possible in 2! ways

The group of boys within itself can be rearranged in 3! ways and
The group of Girls within itself can be rearranged in 3! ways

Total arrangements = 2!*3!*3! = 2*6*6 = 72

Answer: Option C
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Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

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New post 04 Jan 2017, 06:22
2
Bunuel wrote:
In how many different ways can 3 boys and 3 girls be seated in a row of 6 chairs such that the girls are not separated, and the boys are not separated?

A. 24
B. 36
C. 72
D. 144
E. 288


Bunch up the boys together and the girls together. Now we have to arrange 2 groups which we can do in 2! ways.

The boys within themselves can be arranged in 3! ways and the girls within themselves can be arranged in 3! ways.

Total arrangements = 2 * 3! * 3! = 72

Answer (C)

For more on arrangements with constraints, check:
https://www.veritasprep.com/blog/2011/1 ... ts-part-i/
https://www.veritasprep.com/blog/2011/1 ... s-part-ii/
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Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

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New post 04 Jan 2017, 21:45
Condition: girls not separated..and boys are not separated

Count them as 1&1. Now we have 1boys n 1girl..

Arrangements =2!
And arrangements inside 3 girls & inside 3boys is=3! & 3!

Total=2!*3!*3! = 72 option C

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Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

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New post 06 Jan 2017, 10:57
Bunuel wrote:
In how many different ways can 3 boys and 3 girls be seated in a row of 6 chairs such that the girls are not separated, and the boys are not separated?

A. 24
B. 36
C. 72
D. 144
E. 288


We need to determine how many ways to arrange 3 boys and 3 girls in a row of six chairs when the boys must be seated together and the girls must be seated together. Since order matters, we have a permutation problem.

We can arrange the boys and girls as follows:

[B1)-B2)-B(3)] - [G(1)-G(2)-G(3)]

(Note: Since the boys must sit together and the girls must sit together, we have included the boys in one bracket and the girls in one bracket.)

Since we have 2 brackets, we can arrange those 2 brackets in 2! or 2 ways. However, we must account for the individual arrangements of the boys and the girls. The boys can be arranged in 3! or 6 ways and the girls can be arranged in 3! or 6 ways. Thus, the group can be arranged in 2 x 6 x 6 = 72 ways.

Answer: C
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Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

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New post 26 Mar 2018, 13:34
1
Hi Al,

There are a number of ways to do the "math in this question", but here's a way that you might find easy:

The fact that we have 6 chairs in a row means that we'll likely be doing a permutation. We're given the specific rule that the seating will have to be either GGGBBB or BBBGGG.

The first chair can have either a boy or a girl:

6 _ _ _ _ _

Whether it's a boy or a girl, the next two chairs must be the same gender:

6 2 1 _ _ _

Then the next 3 chairs must be the other gender:

6 2 1 3 2 1

Now multiply:

6x2x1x3x2x1 = 72 possibilities.

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Re: In how many different ways can 3 boys and 3 girls be seated in a row &nbs [#permalink] 26 Mar 2018, 13:34
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