Exactly 3 letters be placed into wrong envelopes?
Explanation:
For exactly 3 letters to be placed in wrong envelopes 3 letters must go in their corresponding envelopes.
Chose 3 letters and send them in their corresponding envelopes. The number of ways of doing this = 6C3 × 13 = 20 ways.
Now, the remaining letters can all be sent in wrong envelopes in 3!1-11!+12!-13! = 2 ways.
Note: The number of derangements of a set with n objects is given by the formula = n!1-11!+12!-13!+…+-1nn!.
∴ Required answer = 20 × 2 = 40 ways.
Hence, 40.
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