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Five letters are put into their five addressed envelopes at random. In how many ways do exactly 2 letters reach the correct envelope?

Competition practicePermutations & Combinations

A20
B10
C44
D60

Step-by-Step Solution

Choose the 2 correct letters:

^{5} C_{2} = 10

. The other 3 must all be wrong: a derangement of 3,

D_{3} = 2.10 \times 2 = 20

.

Answer: A) 20

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