Question

30 cars are in a race. In how many different ways can cars finish in the top 3 positions?

Answer 1

Given:

There are 30 cars in a race.

The number of ways that cars finish in the top 3 positions is given as,

$\begin{gathered} ^nP_r=\frac{n!}{(n-r)!} \\ n=30,r=3 \\ ^{30}P_3=\frac{30!}{(30-3)!} \\ =\frac{30!}{27!} \\ =28\times29\times30 \\ =24360 \end{gathered}$

Answer: There are 24360 ways that cars finish in the top 3 positions.