Question

Ajay writes five letters to his five friends and addresses the corresponding .The number of ways can the letters be placed in the envelopes so that at least 2 of them are in the wrong envelopes

Answer 1

The number of possible way of putting 5 letters into 5 envelopes = 5!
Number of ways to place all letters correctly into corresponding envelopes =1
Number of ways to place one letter in the wrong envelope and other 4 letters in the right envelopes =0
It is not possible that only one letter goes in the wrong envelope when 4 letters goes in the right envelope, then remaining one letter also goes in right envelope.

Number of ways to place at least two letters goes in the wrong envelopes = 5! - 0 - 1 = 120 -0-1 = 119