The number of ways in which four different letters can be put in their four addressed envelopes such that atleast two of them are in the wrong envelopes are

Step-by-step solution

Two in wrong envelops = 4 C 2 × 2 ! 1 2 ! = 6 Three in wrong envelops = 4 C 1 × 3 ! 1 2 ! - 1 3 ! = 4 3 - 1 = 8 Four in wrong envelops = 4 ! 1 2 ! - 1 3 ! + 1 4 ! = 12 - 4 + 1 = 9 The total ways = 6 + 8 + 9 = 23