At the school I go to there is only one algebra 2 class, and we went over permutations. There is one word problem that my teacher couldn't explain how they got the answer to. Can anybody explain how they came up with the answer? In how many ways can 5 seniors, 3 juniors, 4 sophomores, and 3 freshmen be seated in a row if a senior must be seated at each end? Assume that the members of each class are distinct.

That's kinda sad. Here goes. There are 15 people so there must be 15 seats [ - ] [ - ] [ - ] [ - ] [ - ] [- ] [ - ] [ - ] [ - ] [ - ] [ - ] [ - ] [ - ] [ - ] [ - ] ------------- There are 5 possiblities (the seniors) for the first seat. If one is sitting there that leaves 4 possibilites for the last seat: [ 5 ] [ - ] [ - ] [ - ] [ - ] [- ] [ - ] [ - ] [ - ] [ - ] [ - ] [ - ] [ - ] [ -] [ 4 ] -------------- That leaves 13 people for the other seats. After each person is seated there is one less possibilitiy, like this: [ 5 ] [ 13 ] [ 12 ] [ 11 ] [ 10 ] [ 9 ] [ 8 ] [ 7 ] [ 6 ] [ 5 ] [ 4 ] [ 3 ] [ 2 ] [ 1 ] [ 4 ] -------------- Then you multiply all those and get 124,540,416,000

Thanks, I get it now. My teacher just read the answer out of book, but couldn't tell us how to work the problem.

Yeah luckily I have pretty good explanations in my books cuz I'm homeschooled. But I wouldn't have been able to tell you that if I hadn't been learning that last week myself.;)