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Five letters are put into five addressed envelopes. In how many ways can this be done so that no letter goes into its own envelope?

Competition practicePermutations & Combinations

A120
B119
C44
D53

Step-by-Step Solution

Derangements:

D_{5} = 5! (1 - 1 + \frac{1}{2 !} - \frac{1}{3 !} + \frac{1}{4 !} - \frac{1}{5 !}) = 60 - 20 + 5 - 1 = 44

. (119 only excludes the all-correct case.)

Answer: C) 44

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