Question

A student club has 20 members. How many ways can the club choose a President, Secretary, and Treasurer?
6,840
8,000
2,280

Answer 1

Where do you think we should start? How many ways can we choose just the president?

Answer 2

20

Answer 3

Precisely. What if we were to ask how many ways to choose the president and the secretary only?

Answer 4

40?

Answer 5

Close, but not quite. This requires combinations and permutations. Since order matter, we need to use permutations. Thus, out of a set of 20, we want to choose 2 people, and permute them. So the answer should really be \[20! \over 2!\]Using this same pattern, do you have a guess as to how many ways we can choose a president, a secretary and a treasurer?

Answer 6

8,000

Answer 7

Not quite. You would want 20P3 which is 6840. I've got to leave for a little bit, but if you want a better explanation, just say so and I'll see to it.