Question

Suppose 56 cars start at a car race. In how many ways can the top 3 cars finish the​ race?

Answer 1

There are 166,320 ways the top 3 cars can finish the race.

Step-by-step explanation:

To calculate the number of ways the top 3 cars can finish the race, we need to use the concept of permutations, specifically the concept of permutations of a subset. Since order matters in this case, we will use permutations. The formula to calculate the number of permutations of a subset is given by P(n, r) = n! / (n-r)!, where n is the total number of cars and r is the number of positions available for the top 3 cars.

With 56 cars starting the race and 3 positions available for the top 3 cars, the calculation would be:

P(56, 3) = 56! / (56-3)! = 56! / 53! = 56 x 55 x 54 = 166,320.

Therefore, there are 166,320 ways the top 3 cars can finish the race.