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?
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?
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