A company is creating three new divisions and seven managers are eligible to be appointed head of a division. How many different ways could the three new heads be appointed?
Before we tackle this problem, it's important to note that, in this situation, the order we pick the managers matters, as each will be heading a different one of the three new divisions. If we had selected three managers A, B, and C from the seven and made the assignments ABC and ACB, those two would not be equivalent, since B and C would be heading different divisions in each.
Now, for the first division, we'll be able to select from any of the
In total, we'll have