Permutations And Combinations Question 335
Question: A person writes letters to six friends and be 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 $ \therefore x-y=454 $
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Answer:
Solution:
$ \therefore x=6!-1=719. $ Now y = number of ways so that all the letters are in wrong envelopes $ =6!{ 1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-\frac{1}{5!}+\frac{1}{6!} } $ [Derangement formula] $ =360-120+30-6+1=265 $
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