There are 10 Letter and 10 correspondingly 10 different Address if the letter are put into envelope randomly then find the Probability that Exactly 9 letter will at the Correct Address?

Exactly 9 letters at the correct address means that the other letter is at the correct address, too. 

Now, the first letter can be sent to any of the 10 addresses. The second letter to any of the remaining 9 addresses and so on.......

So the total number of possibilities is 10*9*8*7*6*5*4*3*2*1, or 10!. Out of these, in only one possibility all the letters will be sent to their rspective addresses. So the probability of sending exactly 9 letters to the correct addresses is 1/10!.