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Exercise 21

Avg difficulty 2.5

A careless payroll clerk is placing employees' paychecks into envelopes that have been pre-labeled. The envelopes are sealed before the clerk realizes he didn't match the names on the paychecks with the names on the envelopes. If there are seven employees, in how many ways could he have placed the paychecks into the envelopes so that exactly three employees receive the correct paycheck?

Keller & Trotter, Applied Combinatorics, Inclusion-Exclusion — Exercises, Exercise 21

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Adapted from Applied Combinatorics © 2006–2025 Mitchel T. Keller, William T. Trotter. Licensed under CC BY-SA 4.0. Source: Applied Combinatorics. Imported at revision 07286c4.