Probability (permutations)

Question

A family consists of a mother, a father, 2 girls and 2 boys. How many different ways can they be arranged in a line if the boys are together and the girls are not?

 

I have no idea how to approach this question, because I'm not sure if its a complementary type question or??

 

Please help!!

Answer 1

Because of the restriction that the two boys must be together, let's treat that as one entity, initially, called BB and we have other entities F, M, G1, G2.

Take a permutation of these FIVE entities--that's 5P5 or 5! ways [such as F M BB G1 G2 or F M BB G2 G1 or ...]

Within any one of those, there are two possible B orders, so we multiply by two, obtaining the final answer
2(5!) which I leave you to finalize as an integer.