Q. There are 10 students on the school debating team. How many different ways can the team choose a president and a secretary?

Ans.

There are 10 choices for the president because every student on the team might be chosen for this position. Once the president is chosen, there are 9 students to choose from for the Secretary.

We can word this as: There are 10 choices for President AND 9 choices for Secretary. So, there are ways for the team to pick their President and Secretary. In this example there were 2 students chosen from 10.

In general, if r objects are chosen from n, then the number of possible permutations, denoted nPr, is

This formula can be written in terms of factorials. Consider a permutation of six objects out of 10. There are 10 ways to choose the first object, 9 ways to choose the second, and so on until all six objects have been selected.

In general,