A person writes letter to six friends and addresses the corresponding envelopes. Let x be the numbers of ways so that at least two of the letters are in wrong envelopes and y be the numbers of ways so that all the letters are in wrong envelopes. Then x - y =

Step-by-step solution

Since only one letters can not be in wrong envelope so that at least two letters are in wrong envelope means all the letters are not in right envelopes. ∴   x = 6 ! - 1 = 720 - 1 = 719 Y = number of ways, so that all the letters are in wrong envelops = 6 ! 1 - 1 1 ! + 1 2 ! - 1 3 ! + 1 4 ! - 1 5 ! + 1 6 ! = 360 - 120 + 30 - 6 + 1 = 265 ∴   x - y = 719 - 265 = 454