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?

1 Answer
Nov 4, 2017



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 #7# managers. For each of those #7# potential options, we'll have #6# remaining managers to choose for the second division head, and for each of those #6#, we'll have #5# to choose from for the final division head.

In total, we'll have #7*6*5=210# potential ways we could pick these heads of each of the three divisions from a pool of #7# managers.