WT Guide: Combinatorics #9

[Guest]

The principal of a high school needs to schedule observations of 6 teachers. She plans to visit one teacher each day for a week, so she will only have time to see 5 of the teachers. How many different observation schedules can she create?

The solution says 6! = 720

My question is why does order matter in this problem? When I solved it my anagram looked like this:

A B C D E F
Y Y Y Y Y N

6! / (5! * 1!) = 6

I tried to frame with reference to some of the earlier problems in the guide where someone is picking a team from a larger group of people (ie. group of 7, how many teams of 4 can be made). I think I"m missing something in the wording that makes this problem different.

Thanks

[StaceyKoprince]

The key is that the problem says "how many different observation schedules can she create?" Are these the same schedule or different schedules:
- visit Ms. X's class on Monday and Mr. Y's class on Tuesday
- visit Mr. Y's class on Monday and Ms. X's class on Tuesday

Same teachers, but I see them on different days. Those are two different schedules - I have to be in different places on Monday and Tuesday depending upon which one I do.

That's not the same thing as asking "how many different sets of 5 teachers can she visit?" Then, I only care that she visits, say, teachers X, Y, Z, A, and B, in any order, but she doesn't visit teacher C.

As much as possible for combinatorics, try to place yourself mentally in the situation and make sure you stick to exactly what the question is asking - then see whether order matters or not.