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,
[tex]P = \ ^{n}P_r=\ ^{27}P_3\\P = \dfrac{n !}{(n-r)!}\\\\P = \dfrac{27!}{(27-3)!}\\\\P=\dfrac{27!}{24!}\\\\P = 27\times 26\times 25\\\\P= 17550[/tex]
Therefore, total number of order are 17550.
Hence, this is the required solution.
