Question

I need help with a simple word problem!:How many different 1st,2nd, and 3rd place finishers are possible for a race with 6 people in it?

Answer 1

120 ways

Explanation:

We would be using permutation as the position each finihes is considered.

Total people in the race = 6

There are 3 place finishers:

The number of possilble ways = 6P3

$6P3\text{ = }\frac{6!}{(6-3)!}$$\begin{gathered} =\frac{6!}{3!}=\frac{6\times5\times4\times3!}{3!} \\ =\text{ }6\times5\times4| \\ =\text{ 120 ways} \end{gathered}$