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A group of four boys and three girls is to be seated in a row. how man

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A group of four boys and three girls is to be seated in a row. how man  [#permalink]

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New post 28 Mar 2018, 22:43
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A group of four boys and three girls is to be seated in a row. how many such arrangements are possible where no girls sit together ?

A. 144
B. 288
C. 576
D. 720
E. 1440

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Re: A group of four boys and three girls is to be seated in a row. how man  [#permalink]

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New post 29 Mar 2018, 03:01
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The 4 boys can be seated in 4! Ways.
The 3 girls can be seated between boys .
We have to selected 3 positions from 5 available.
5C3.
Ordering =3!.

Total number of ways = 4!*5C3*3! = 1440. Answer E

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A group of four boys and three girls is to be seated in a row. how man  [#permalink]

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New post 29 Mar 2018, 04:06
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rishabhmishra wrote:
A group of four boys and three girls is to be seated in a row. how many such arrangements are possible where no girls sit together ?

A. 144
B. 288
C. 576
D. 720
E. 1440

Source:- Experts global.


Between every two BOYS there must be A MAXIMUM OF one GIRL hence we the the arrangements will look as follows

- B - B - B - B -

But since there are only 3 girls and 5 places available for them (shown by dashes above) so we need to select those 3 places for the girls out of 5

Selection of 3 places out of 5 for the girls = 5C3
Arrangement of the girls on 3 selected places = 3!
Arrangement of the boys on 4 places = 4!

Total Favourable outcomes = 5C3*3!*4! = 60*24 = 1440

Answer: option E
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A group of four boys and three girls is to be seated in a row. how man  [#permalink]

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New post 04 Apr 2018, 06:12
GMATinsight wrote:
rishabhmishra wrote:
A group of four boys and three girls is to be seated in a row. how many such arrangements are possible where no girls sit together ?

A. 144
B. 288
C. 576
D. 720
E. 1440

Source:- Experts global.


Between every two BOYS there must be A MAXIMUM OF one GIRL hence we the the arrangements will look as follows

- B - B - B - B -

But since there are only 3 girls and 5 places available for them (shown by dashes above) so we need to select those 3 places for the girls out of 5

Selection of 3 places out of 5 for the girls = 5C3
Arrangement of the girls on 3 selected places = 3!
Arrangement of the boys on 4 places = 4!

Total Favourable outcomes = 5C3*3!*4! = 60*24 = 1440

Answer: option E


I am trying to understand why are you assuming 9 spaces to be filled? are we not supposed to fill 7 spaces (4 boys and 3 girls)? Kindly help me understand!
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A group of four boys and three girls is to be seated in a row. how man  [#permalink]

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New post 04 Apr 2018, 09:08
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I would be happy to explain.

Since the condition is that no 2 girls should sit together, we should ensure that there would be at least one boy between any 2 girls.
Now the 4 boys have already been placed in 4! ways.

After that we need to find the slots which can be filled by girls so that no 2 girls are together,

- B - B - B - B -

If you observe carefully, if the girls are made to sit on the 5 blanks seat represented by -, then no 2 girls would be together.

So as we have 3 girls , we need to select 3 blanks seat out of 5 blanks as mentioned above, which can be done in 5C3 ways.
After the selection of 3 blanks seats, the girls can be arranged in 3! ways.

Hence the total number of ways would be 4!*5C3*3! = 1440.

I hope it is clear now, feel free to ask further in case of any doubts.

SalmanDard wrote:
GMATinsight wrote:
rishabhmishra wrote:
A group of four boys and three girls is to be seated in a row. how many such arrangements are possible where no girls sit together ?

A. 144
B. 288
C. 576
D. 720
E. 1440

Source:- Experts global.


Between every two BOYS there must be A MAXIMUM OF one GIRL hence we the the arrangements will look as follows

- B - B - B - B -

But since there are only 3 girls and 5 places available for them (shown by dashes above) so we need to select those 3 places for the girls out of 5

Selection of 3 places out of 5 for the girls = 5C3
Arrangement of the girls on 3 selected places = 3!
Arrangement of the boys on 4 places = 4!

Total Favourable outcomes = 5C3*3!*4! = 60*24 = 1440

Answer: option E


I am trying to understand why are you assuming 9 spaces to be filled? are we not supposed to fill 7 spaces (4 boys and 3 girls)? Kindly help me understand!
"B-B-B-B"

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Re: A group of four boys and three girls is to be seated in a row. how man  [#permalink]

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New post 04 Apr 2018, 22:29
BGBGBGB <- this fulfills 4 boys and 3 girls and no girls sit together. So 4!x3!=144 which is A???
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Re: A group of four boys and three girls is to be seated in a row. how man  [#permalink]

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New post 07 Apr 2018, 18:43
Hi I

You are right , this fulfills the criteria, but this covers some of the favourable cases, not all of them.
We need all the favourable cases, which can be found as explained above.
Feel free to ask again if not fully satisfied.

Regards
SalmanDard wrote:
BGBGBGB <- this fulfills 4 boys and 3 girls and no girls sit together. So 4!x3!=144 which is A???

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Re: A group of four boys and three girls is to be seated in a row. how man  [#permalink]

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New post 08 Apr 2018, 09:14
I think this question can be solved even using jst permutation. However I am not able to arrive at the answerusing jst permutations. Can someone please help me?

The concept that I used is 7!-(all combinations wth 2 girls together) - (all combinations wth 3 girls together)

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Re: A group of four boys and three girls is to be seated in a row. how man  [#permalink]

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New post 13 Jun 2018, 07:52
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aviejay wrote:
I think this question can be solved even using jst permutation. However I am not able to arrive at the answerusing jst permutations. Can someone please help me?

The concept that I used is 7!-(all combinations wth 2 girls together) - (all combinations wth 3 girls together)

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Hi

Let me try to explain this,
The statement should be 7! - [6! 2! 2! + 5! 3!] = 5040 - [2880 + 720] = 1440

Total number of ways in which 7 students can sit is 7!.

Total number of ways in which 2 girls sit together - 6! 2! 2! [(GG)BBBBG, we multiply by 2! once because 2 girls can interchange their place and we multiply 2! again because (GG)G can also interchange their place].

Total number of ways in which 3 girls sit together - 5! 3! [ (GGG)BBBB]

Hope I was able to clear your doubt. :thumbup:
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Re: A group of four boys and three girls is to be seated in a row. how man  [#permalink]

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New post 13 Jun 2018, 23:46
There are four boys and three girls.
Condition: No girls should sit together.
In order to make sure that the condition is satisfied, we order the boys first and then the girls in the gaps between the boys.

As the number of boys here is 4. They can be arranged in 4! ways.
__B__B__B__B__
We have 5 gaps between the boys. ( In general, gaps will be number of things + 1 )
We need to first choose 3 gaps for the girls, this can be done in 5C3 ways.
Then arrange the girls, which can be done in 3! ways.
Total: 4! X 5C3 X 3! ( We need to multiply the events here )
Total = 1440.
Option E
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Re: A group of four boys and three girls is to be seated in a row. how man &nbs [#permalink] 13 Jun 2018, 23:46
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