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Chapter 11: Problem 57

In a race in which six automobiles are entered and there are no ties, in how many ways can the first four finishers come in?

Short Answer

Expert verified
The first four finishers can come in 360 different ways in a six-automobile race.

Step by step solution

01

Understand Permutation Formula

Permutation of n items taken r at a time can be calculated using the following formula: \(P(n, r) = n! / (n-r)!\). In our problem, n is 6 (as there are 6 automobiles) and r is 4 (as we need to find out the number of ways the first four automobiles can finish).
02

Substitute in the Permutation Formula

Put the values of n and r in the permutation formula: \(P(6, 4) = 6! / (6-4)!\). Now calculate the factorial of 6 and 2.
03

Calculate Factorials

Factorial of a number is the product of all positive integers up to that number. Factorial 6 is calculated as: 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720 and factorial 2 is calculated as: 2! = 2 * 1 = 2.
04

Solve the Permutation

Replace the factorials with their results in the permutation formula (720/2) to find the number of ways.
05

Final Calculation

Perform the division to find out the final answer of the permutation. 720/2 = 360

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