A) 719
B) 265
C) 454
D) None
Correct Answer: C
Solution :
[c] If all the letters are not in the right envelopes, then at least two letters must be in wrong envelopes. \[\therefore \,\,\,x=6!-1=719.\] Now y = number of ways so that all the letters are in wrong envelopes \[=6!\left\{ 1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-\frac{1}{5!}+\frac{1}{6!} \right\}\] [Derangement formula] \[=360-120+30-6+1=265\] \[\therefore x-y=454\]You need to login to perform this action.
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