In how many ways can 8 boys and 5 girls be assigned seats in a row containing 13 seats if:
1) There are no restrictions.
2) The girls must be seated in the first 5 seats.
3) Thomas must be seated in the first seat and Jacob must be seated in the last seat.
First things first --- do I use the permutation?
1) prob of girls x prob of boys? p(5,5) * p(8,8)
2) G G G G G B B B B B B B B
p(5,5)* p(8,8)
3) B G G G G G G G G G G G B
p (2,2) * p(11,11)
11 girls in between and 2 boys
of course it's permutations, since order matters.
#1. Not P(8,8)*P(5,5)
That only works if all 8 boys sit together, and also the girls.
Take a look at permutations with duplicates. You have 13 students, so you will get 13!
#2. This is your P(5,5)*P(8,8)
#3. There are not 11 girls -- only 5. But there are 11 other students, so your answer is correct.