Example Problem from Notes: Friday, 1/16/15
We had the problem, "5 guys go to a coat check. There are 60 coats. How many ways may they be given 5 coats if they simultaneously get them?" We solved the problem by doing 60x59x58x57x56 or P(60,5). I am confused as to why we use "n pick k" here and not "n choose k." Doesn't the fact that they get the coats all at once mean that order does not matter?
Soniakumr: Jan. 21, 2015, 11:18 p.m.
If you treat each person as a generation of choice that has to be made then the first person has 60 coats to choose from and the next person has 59 and so on until you get to the 5th person who has 56 coats to chose from.
weisbart: Jan. 22, 2015, 9:51 p.m.
Perfect Soniakumr. You got it. The point is that $60\choose 5$ will count all the ways you can get 5 coats, but it doesn't give you all the ways you can give them to the five people. One way to think about it is that you choose the five coats and then order them. Putting them in order corresponds to giving them to the people. I like using five generations of choices though, one for each person. Either way, you get the same answer.