SOLUTION: 13 pepole are entered in a race. if there is no ties, in how many ways can the first three places come out?

Question 194347: 13 pepole are entered in a race. if there is no ties, in how many ways can the first three places come out?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Since order does matter, we must use the permutation formula:

Start with the given formula

Plug in and

Subtract to get 10

Expand 13!

Expand 10!

Cancel

Simplify

Now multiply 13*12*11 to get 1,716

So 13 choose 3 (where order does matter) yields 1,716 unique permutations

This means that there are 1,716 ways for 3 people to finish in the first three places.

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