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Question

Supposing 4 letters are placed in 4 different envelopes. In how many ways can they be taken out from their original envelopes and distributed among the 4 different envelopes so that no letter remains in its original envelope?

A
7
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B
8
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C
9
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D
None of these
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Solution

The correct option is D 9
Using the formula for the number of derangement that are possible out of 4 letters in 4 envelopes, we get the number of ways as
4!(11+12!13!+14!)
= 24(11+1216+124)
= 24(11+1(12)2(12)1(4)6(4)+124)
=24(124+124)
= 24×924
=9

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