Puzzle - 8

Last I had sent this puzzle

I had decided to send some (10 to be precise) New Year cards by snail mail. I wrote down the names and the addresses on the envelopes and details on the cards. But then as usual lights went off. It was dark in the night and I could not put the cards inside the envelopes fearing that they may be sent to the wrong person. I just wondered putting them in the envelopes at random and calculating probability of all of them being kept in the right envelopes or in wrong envelops.  It is difficult one so I asked one of my friend Prof. Ram Chandra Tiwari He tells me it is easy and there is a formula to calculate it. The probability of all of them going right is 1/10! Or 1 divided by 362880; it is almost zero. The probability of putting all of them in wrong envelopes is 0.36788 that is more than one third. But he asked me to tell him the probability of only one card being kept in the wrong envelope. I have not been able to do that. Can you help me?

He says that it does not require any formula. I am still in a fix. 

The answer is that the probability of sending one of them in the wrong envelope is zero. If one card is kept in the wrong envelope then the card of that envelope will have to be kept in another envelope which is not meant for it. ie at least two cards have to be kept in the wrong envelopes one card can never be kept in the wrong envelope 

Sa’ad, a barrister in Toronto, informs me that candidates nowadays are asked questions and are hired according to their answers. This is one of the questions. Make a guess.

Continued >----