Permutations And Combinations Question 335
A person writes letters to six friends and find the number of ways so that at least two of the number of ways so that all the letters are in wrong envelopes. Then $ x - y = $
Options:
A) 719
B) 265
C) 454
D) None
Correct Answer: C [c] If all the letters are not in the right envelopes, then at least one letter must be in the wrong envelope.
$ \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] $ =720-120+30-6+1=625 $ $ \therefore x-y=454 $
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Solution:
BETA
