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Three pairs of siblings, each pair consisting of one girl [#permalink]
05 Aug 2012, 03:32

5

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00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

40% (03:23) correct
60% (01:49) wrong based on 126 sessions

Three pairs of siblings, each pair consisting of one girl and one boy, are randomly seated at a table. What is the probability that all three girls are seated on the left of their boy siblings?

Re: Three pairs of siblings, each pair consisting of one girl [#permalink]
05 Aug 2012, 04:08

7

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Expert's post

1

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EvaJager wrote:

Three pairs of siblings, each pair consisting of one girl and one boy, are randomly seated at a table. What is the probability that all three girls are seated on the left of their boy siblings?

Notice that we need a girl to be to the left of her sibling, but not necessarily right to the left of him (meaning that if B and G are siblings, then GB arrangement as well as for example G*B arrangement is possible).

Now, the probability that one particular sibling is seated that way is 1/2 (a girl can be either to the left of her sibling or to the right), the probability that two siblings are seated that way is 1/2*1/2 and the probability that all three siblings are seated that way is 1/2*1/2*1/2=1/8.

Re: Three pairs of siblings, each pair consisting of one girl [#permalink]
05 Aug 2012, 04:35

Bunuel wrote:

EvaJager wrote:

Three pairs of siblings, each pair consisting of one girl and one boy, are randomly seated at a table. What is the probability that all three girls are seated on the left of their boy siblings?

Notice that we need a girl to be to the left of her sibling, but not necessarily right to the left of him (meaning that if B and G are siblings, then GB arrangement as well as for example G*B arrangement is possible).

Now, the probability that one particular sibling is seated that way is 1/2 (a girl can be either to the left of her sibling or to the right), the probability that two siblings are seated that way is 1/2*1/2 and the probability that all three siblings are seated that way is 1/2*1/2*1/2=1/8.

Answer: D.

By far the fastest and most elegant solution!

Those who want to play with combinatorics are invited to provide an alternate solution. _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: Three pairs of siblings, each pair consisting of one girl [#permalink]
05 Aug 2012, 23:23

2

This post received KUDOS

EvaJager wrote:

Three pairs of siblings, each pair consisting of one girl and one boy, are randomly seated at a table. What is the probability that all three girls are seated on the left of their boy siblings?

Place the first pair of siblings - we have 6 possibilities for one of them, and 5 for the other one; this gives 6*5, but we have to divide by 2, as only in half of them, the girls will sit on the left of her brother. So, 6*5/2=15 possibilities. To place the second pair of siblings - similarly, we have 4*3/2=6 possibilities. Finally, for the last and third pair - 2*1/2 = 1 possibility.

Therefore, the requested probability is 15*6/6!= 3*5*6/(2*3*4*5*6)=1/(2*4) = 1/8.

Answer D. _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: Three pairs of siblings, each pair consisting of one girl [#permalink]
06 Aug 2012, 21:45

Thanks Bunuel, you once again showed that in GMAT in most cases it is more logical thinking than doing quants. I have tried this one with different approaches but still could not come up with solution, but after your explanation it seems so easy and i wonder how i could not come up myself.

Thanks!!! _________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Re: Three pairs of siblings, each pair consisting of one girl [#permalink]
07 Nov 2012, 04:27

1

This post received KUDOS

Expert's post

BN1989 wrote:

EvaJager wrote:

EvaJager wrote:

Therefore, the requested probability is 15*6/6!= 3*5*6/(2*3*4*5*6)=1/(2*4) = 1/8.

Answer D.

Aren't there only 5! total arrangements around a table for 6 people?

We are not told that these 6 are seated around a table, so we don't have circular arrangement. The question implies that they are seated like in a row. _________________

Re: Three pairs of siblings, each pair consisting of one girl [#permalink]
08 Nov 2012, 10:06

EvaJager wrote:

EvaJager wrote:

Three pairs of siblings, each pair consisting of one girl and one boy, are randomly seated at a table. What is the probability that all three girls are seated on the left of their boy siblings?

Place the first pair of siblings - we have 6 possibilities for one of them, and 5 for the other one; this gives 6*5, but we have to divide by 2, as only in half of them, the girls will sit on the left of her brother. So, 6*5/2=15 possibilities. To place the second pair of siblings - similarly, we have 4*3/2=6 possibilities. Finally, for the last and third pair - 2*1/2 = 1 possibility.

Therefore, the requested probability is 15*6/6!= 3*5*6/(2*3*4*5*6)=1/(2*4) = 1/8.

Re: Three pairs of siblings, each pair consisting of one girl [#permalink]
12 Feb 2014, 03:09

Bunuel wrote:

EvaJager wrote:

Three pairs of siblings, each pair consisting of one girl and one boy, are randomly seated at a table. What is the probability that all three girls are seated on the left of their boy siblings?

Notice that we need a girl to be to the left of her sibling, but not necessarily right to the left of him (meaning that if B and G are siblings, then GB arrangement as well as for example G*B arrangement is possible).

Now, the probability that one particular sibling is seated that way is 1/2 (a girl can be either to the left of her sibling or to the right), the probability that two siblings are seated that way is 1/2*1/2 and the probability that all three siblings are seated that way is 1/2*1/2*1/2=1/8.

Answer: D.

Hi Bunuel,

first sibling can be seated in 1/2 ways. but how do we come about the second sibling probability of 1/2 ? I am bit confused here, can you explain please ?

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