Question

There are 5 swimmers in a race. There will be a first-place, a second-place, and a third-place prize awarded. In how many different ways can the 3 prizes be awarded?

Answer 1

Answer:

Step-by-step explanation:

This is a permutation problem.  There are 5 swimmers in the race, and any combination of 3 will finish in the first 3 places.  The formula will look like this:

₅P₃ = $\frac{5!}{(5-3)!}$  which will expand to

₅P₃ = $\frac{5*4*3*2*1}{2*1}$  and when the 2 * 1 cancels out between the numerator and the denominator, you're left with simply:

₅P₃ = 5 * 4 * 3

which is 60