This, too, is taught in an age-appropriate manner which never introduces the concept of a factorial! The solution is as follows:

How many ways to choose a president? (8) After you choose the president, how many people are available to be vice-presidents? (7) So the answer is 8 X 7 = 56. |

The high school text book solution to this problem is:

Given that N = number of people and C = number being chosen: P = N!/(N-C)! = 8!/6! = (8 X 7 X 6 X 5 X 4 X 3 X 2 X 1)/ (6 X 5 X 4 X 3 X 2 X 1) = 40320/720 = 56 |

Correct, but much tougher to understand! Also, the first technique gives the student some insight into what is going on, where the second technique merely presents an equation that produces correct results but without a clear relationship to the problem. The second approach encourages students to take equations on faith and to "turn the crank" to get solutions. To use this second method, the student must also memorize the equation. The first technique involves no memorization, just simple logic!