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Chapter 1: Problem 3

Twenty workers are to be assigned to 20 different jobs, one to each job. How many different assignments are possible?

Short Answer

Expert verified
There are \(2,432,902,008,176,640,000\) different ways to assign 20 workers to 20 different jobs.

Step by step solution

01

Identify the number of objects and positions

In this problem, we have 20 workers doing 20 different jobs. So, we have 20 objects (workers) and 20 positions (jobs) to fill.
02

Calculate the permutations

To calculate the total number of permutations for this problem, we use the formula n! (n-factorial), where n is the number of objects or positions. In this case, n = 20. The formula for permutations is: \[ n! = 1 * 2 * 3 * \cdots * 20 \]
03

Evaluate the expression

To find the answer, we need to calculate 20!. \[ 20! = 1 * 2 * 3 * \cdots * 20 = 2,432,902,008,176,640,000 \]
04

State the solution

There are 2,432,902,008,176,640,000 different ways to assign 20 workers to 20 different jobs.

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