In a task assignment situation, in how many different ways can five jobs be assigned to five machines if each job must be assigned to each machine and each machine must be assigned one job?
A)1
B)5
C)25
D)120
E)3,125

Question

Quizplus · Accepted Answer

This is a permutation problem because the order in which the jobs are assigned to machines matters. There are 5 options for the first job, 4 for the second, 3 for the third, 2 for the fourth, and 1 for the last, so the total number of ways is 5! (5 factorial), which is 5 x 4 x 3 x 2 x 1 = 120.

In a Task Assignment Situation, in How Many Different Ways