In the problem we are asked to find the probability that 2 girls are between a pair of boys. Hence we can generate the following arrangements:
b g g b g g b g g g g -- arrangement 1
In this situation, we are only interested on the part between the boys, hence we create a boundary just for the sake of calculation.
|b g g b g g b| g g g g -- arrangement 2
To solve this problem, we use the Combination formula: nCr = n! / n! (n-r)!
We can see in the above arrangement 2, that for the 3 boys there are 7 places which he can take, therefore:
7C3 = 7! / 7! (7-3)!
7C3 = 35
While the total places the 3 boys can take are 11 based on arrangement 1, therefore:
11C3 = 11! / 11! (11-3)!
11C3 = 165
Therefore the probability that two girls will be between two boys is:
Probability = 35 / 165
Probability = 0.2121
Therefore there is a 21.21% probability that 2 girls is between 2 boys.
