a deck of n numbered cards is thoroughly shuffled and the cards are inserted into n numbered cells one by one. If card no.'i' falls in the cell 'i', we count it as a match, otherwise not. Find mean and variance of total no. of such matches.
Number of ways to allot n umbrellas to n people such that no one gets their own umbrella is given by the dearrangrments formula which is kind of complicated to type but you can look it up.
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