At a local elementary school, a principal is making random class assignments for her 8 teachers. Each teacher must be assigned to exactly one job. In how many ways can the assignment be made?
Question
At a local elementary school, a principal is making random class assignments for her 8 teachers. Each teacher must be assigned to exactly one job. In how many ways can the assignment be made?
Solution
This is a permutation problem. The principal has 8 options for the first teacher, 7 options for the second, 6 for the third, and so on, until there is only 1 option for the last teacher.
So, the total number of ways the principal can assign the teachers is 8765432*1 = 40,320 ways.
This is because the order in which the teachers are assigned matters, making it a permutation rather than a combination.
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