How many was can 10 people come in 1st, 2nd and 3rd place in a race once around the track?

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Answer 1 · 2016-02-07T03:29:11

Since order matters in this problem, we use the permutation formula.

Assuming P represents the number of outcomes, n the number of competitors and r the number of places to be awarded.

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

P = #(10!)/((10 - 3)!)#

P = #(10!)/(7!)#

Calculating using a calculator:

P = 720

There are 720 different outcomes possible in the race.