Question

There are 27 runners competing in a marathon. In how many different orders could the 1st, 2nd, and 3rd place medals be received

Answer 1

Given :

There are 27 runners competing in a marathon.

To Find :

In how many different orders could the 1st, 2nd, and 3rd place medals be received.

Solution :

Let, N is the number of outcomes and r is the number of positions ( i.e 3)

So,

`P = \ ^(n)P_r=\ ^(27)P_3\\P = (n !)/((n-r)!)\\\\P = (27!)/((27-3)!)\\\\P=(27!)/(24!)\\\\P = 27* 26* 25\\\\P= 17550`

Therefore, total number of order are 17550.

Hence, this is the required solution.