suppose 59 cars start at a car race, how many ways can the top car finish the race?
540
To determine the number of ways that the top car can finish the race, we need to calculate the possible permutations of the 59 cars.
Permutations represent the different arrangements of objects in a sequence. In this case, we want to find the number of permutations of the 59 cars.
Since we are considering the top car's position, it can be any one of the 59 cars initially. For the second position, it can be any one of the remaining 58 cars, and so on.
To calculate the total number of permutations, we can use the formula for permutation:
nPr = n! / (n - r)!
Where n is the total number of objects (cars in this case), r is the number of objects being arranged (in this case, positions in the race), and "!" represents the factorial of a number. The factorial of a number is the product of that number and all positive integers below it.
In this case, we want to calculate 59P1, as we are only considering the first position (top car). Using the permutation formula:
59P1 = 59! / (59 - 1)!
= 59! / 58!
= 59.
Therefore, there are 59 different ways the top car can finish the race.