Given three members of a group -- Alice, Bob, and Carol -- in how many ways can these three be chosen to be the three officers (president, secretary, and treasurer) of the group, assuming no person holds more than one job?
Alice, Bob, Carol:
3 ways to choose the person for the first job, then two ways, and finally one way.
3 * 2 * 1 = 6 ways.
If alice goes first
Alice can be 3 choices
Bob can have 2 choices
Carol can have 1 choice
In other words, it's just 3!
um... what. So Alice can have 3 choices, bob has 2, and carol has 1. That means its 6 ways..... so it's not just 3...
I do not understand what you are confused on. 3! means 3 * 2 * 1. Also, you cannot apply factorial to other problems like this (I just used it to represent my answer).