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

Question

asked May 15, 2023 72.6k views

2 Answers

Tyty · Answer 1 · 2023-05-21T14:22:47+0000

Given:

There are 30 cars in a race.

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

$\begin{gathered} ^nP_r=(n!)/((n-r)!) \\ n=30,r=3 \\ ^(30)P_3=(30!)/((30-3)!) \\ =(30!)/(27!) \\ =28*29*30 \\ =24360 \end{gathered}$

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