In how many ways can 4 girls and 3 boys sit in a row such that just the girls are to sit next to each other? Answer: 288
Please explain how to get this.
I understand that we have
GGGG => 4 girls next to each other
B B B => 3 boys
but how do you put them together and work out the number of possible ways. They are different so not identical
Best Answer
We can have:
GGGGBBB, BGGGGBB, BBGGGGB, BBBGGGG
(There are four ways to place a group of four consecutive girls in a row of seven.
The girls can be permuted in each case $4!$, and so can the boys $(3!)$.
$$\bf 4\times 4!\times 3! = 576$$
NOTE If the intention of the author was that girls must sit next to a girl, and boys next to a boy, then there are only two ways to place the group of girls: GGGGBBB, BBBGGGG.
In that case, we have $2 \times 4!\times 3! = 288$.