Question

There are 42 members on the board of directors for a certain non-profit institution. lf they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible?

Answer 1

2,686,320

Explanation:

This is a classic Permutations problem (the order of selection matters - where the first person selected is the Chairperson, the next the First Vice Chair, and so on, whereas in a classic Combinations problem, like a poker hand, it doesn't matter which card you got first, second, etc.)

We have 42 people and we're looking for 4 jobs to be filled. Which is:

`P_(42,4)=(42!)/((42-4)!)=(42!)/(38!)=(42xx41xx40xx39xx38!)/(38!)=(42xx41xx40xx39)=2,686,320`