A race has 125 Participants, in how many ways can the runners come in 1st, 2nd and 3rd place?

Question

A race has 125 Participants, in how many ways can the runners come in 1st, 2nd and 3rd place?

Answer 1

This is a simple counting principle problem.

 

125 people can possibly come in 1st.

Once one is the winner, only 124 can come in 2nd

And now only 123 remain to come in 3rd

 

Your total is simply 125*124*123=1,906,500 different ways.

 

This is also known as a permutation, where order matters.  You can use the formula for permutations to get the same answer:

 

₁₂₅P₃ = 125!/(125-3)!