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

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

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!] " . 

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

Badiuddin