In how many different orders can 5 runners finish a race if

In how many different orders can 5 runners finish a race if no ties are allowed?

Solution

5!

=5*4*3*2*1

=120

SInce there are 5 runners there are 5 possibilities for first place.

The possibilities for second are 4 because there are 4 runners left to take second.

That makes a total of 20 possibilities for first and second place winners.

Third place will have 3 possible runners after first place and second have finished and fourth and fifth, four and five. That makes a total of 120 possibilities for first,second,third,fourth,and fifth place.