# Eight letters are to be kept in 8 envelopes. Find probability that at least one letter is kept in right envelope?

148 Points
14 years ago

dear pratik

number of ways  of at least one letter is kept in right envelope(n)

n= total ways - number of ways when all letter kept in wrong envelope

n  =8!          -               8![1-1/1! +1/2! -1/3! .........+1/8!]

So probability =n/8!

calculate value of n and put here

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Pratik Sharma
18 Points
14 years ago

Thats good, but i cant understand how the "number of ways when all letter kept in wrong envelope " came as " 8![1-1/1! +1/2! -1/3! .........+1/8!] " .

148 Points
14 years ago

Dear pratik

this is theorem proof is not in IIT JEE syllabus

If n letter are to be kept in n envelope such that no letter kept in  right envelope so number of ways=

n![1-1/1!+ 1/2! -1/3! +..........(-1)n 1/n!)]

Regards