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

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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) About Me  (Show Source):
You can put this solution on YOUR website!

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




n%21%2F%28n-r%29%21 Start with the given formula



13%21%2F%2813-3%29%21 Plug in n=13 and r=3



13%21%2F10%21 Subtract 13-3 to get 10



Expand 13!
%2813%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F10%21



Expand 10!




Cancel



13%2A12%2A11 Simplify




1716 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.