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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 the 20 workers to the 20 jobs.

Step by step solution

01

Understand the problem

In this problem, we have 20 workers and 20 jobs. Each worker can be assigned to any of the 20 jobs, and each job needs a worker. We need to determine the number of different ways to assign workers to jobs. Step 2: Calculate permutations
02

Calculate permutations

To find out how many different ways to assign the workers to the jobs, we will use permutations. For the first job, there are 20 workers to choose from. Once the first job is filled, there are 19 remaining workers to assign to the second job. Similarly, there will be 18 workers left for the third job, and so on. Use the formula for permutations: Number of Assignments = n! = 20! Step 3: Compute the factorial
03

Compute the factorial

Now, calculate the factorial: Number of Assignments = 20! = 20 脳 19 脳 18 脳 ... 脳 2 脳 1 Step 4: Calculate the total
04

Calculate the total

Finally, perform the multiplication to get the total number of different assignments: Number of Assignments = 20! = 2,432,902,008,176,640,000 Thus, there are 2,432,902,008,176,640,000 different ways to assign the 20 workers to 20 jobs.

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Most popular questions from this chapter

Argue that $$ \begin{array}{r} \left(\begin{array}{c} n \\ n_{1}, n_{2}, \ldots, n_{r} \end{array}\right)=\left(\begin{array}{c} n-1 \\ n_{1}-1, n_{2}, \ldots, n_{r} \end{array}\right)+\left(\begin{array}{c} n-1 \\ n_{1}, n_{2}-1, \ldots, n_{r} \end{array}\right) \\ +\cdots+\left(\begin{array}{c} n-1 \\ n_{1}, n_{2}, \ldots, n_{r}-1 \end{array}\right) \end{array} $$ HINr: Use an argument similar to the one used to establish Equation (4.1).

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