This is the question I am attempting.
If there are 4 girls and 4 boys going to a movie theatre, in how many different arrangements could they sit together if…
a) the first and last seats were occupied by girls
and
b) all the girls want to sit together?
And this is what I have done:
a) There are 4 girls, and the first and last spaces are taken by girls in 4P2 (nPr) ways. After the 2 girls have taken a seat, there are now 6! ways in which the rest of the group can sit (4 boys and 2 girls remaining).
Meaning the total number of ways for them to be seated in 4P2 * 6! (I'm not sure if this is correct)
b) All the girls want to sit together this time. If we take all 4 of the girls as one entity then we will have 4 + 1 = 5 total entities to shuffle around. Therefore this seating arrangement has 5! ways and the 4 girls can be arranged in 4! ways.
Meaning the total number of ways for them to be seated in 5! * 4!
I would like to know if my analysis and thought process is correct.