A company has 30 salespeople. A board member at the company asks for a list of the top 5 salespeople, ranked in order of effectiveness. How many such rankings are possible?

To solve this problem, we need to use the concept of permutations in combinatorics. A permutation is an arrangement of objects in a specific order.

The number of permutations of n distinct objects taken r at a time is given by the formula:

P(n, r) = n! / (n-r)!

where "!" denotes factorial, which is the product of all positive integers up to that number.

In this case, we have 30 salespeople (n = 30) and we want to rank the top 5 (r = 5).

So, we can plug these values into the formula:

P(30, 5) = 30! / (30-5)!

Calculating this will give us the number of possible rankings of the top 5 salespeople out of 30.