3 girls and 4 boys were standing in a circle. What is the probability that two girls are standing together, but the third one is not next to them?

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- Nov 1st 2009, 12:10 PMAquafinaBoys and Girls
3 girls and 4 boys were standing in a circle. What is the probability that two girls are standing together, but the third one is not next to them?

- Nov 1st 2009, 06:37 PMANDS!
Question doesn't make any sense. One what is not with them?

- Nov 1st 2009, 09:30 PMAquafina
I have edited it to be clearer. This is what I did, there are 7 arrangements that 2 girls can stand in:

GG***** the other girl can stand in 4 different places here

*GG**** other girl in 3 places

**GG*** 3

***GG** 3

****GG* 3

*****GG 4

So in total: 2x(4+3+3) = 20

Is this correct? Do you have any other methods that you could show? - Nov 1st 2009, 09:35 PMRobb
- Nov 1st 2009, 09:39 PMAquafina
- Nov 4th 2009, 11:30 AMjt5271
probability = no. ways you can arrange two girls together without third being adjacent / total no ways to arrange 3 girls and 4 boys in circle.

B- boy

G-girl

BGGB - C

First part is synomymous to arranging B,B,G,C on a straight line = 4!/2! = 12

Second part = 7!/3!4! = 35

Prob = 12/35