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Oxbridge maths question

I'm preparing for an interview, but I'm having difficulty in asnwering this questions....
"3 girls and 4 boys were standing in a circle. What is the probability that the two girls are together but one is not with them?"
Reply 1
Avatar for dark_link
dark_link
well i'm not sure what the answer is, but approach it like this - is it a circle made up of 7 places. in order for two girls to be together and the third on their own, what are the possible arrangements.

Boy
Girl >This pattern must be the case in all the combinations. the reminaing
Girl >girl and two boys can be arranged in any manner around them.
Boy

the probability of this occurring is worked out with the probability of a boy being in a space 4/7 initially and 3/7 for a girl. each time a space is used up, reduce the denominator by one, and the numerator is the no of girls or boys left.

hmm... yeah something like that.
Reply 2
Avatar for datr
datr
12
Yes that seems to work:

Starting at the first place in the circle:

47×36×25×34=335\frac{4}{7} \times \frac{3}{6} \times \frac{2}{5} \times \frac{3}{4} = \frac{3}{35}

Times this by 7 as the same probabilities occur if you have this group at any point. So p = 3/5.

Or by looking at the possible arrangements:

BBBGGBG GBBGGBB BGBBGGBB

BBBBGGG BGBGBGB

So the probability is 3/5.

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