39. A group of n people went to a theater, and each of them left his coat and his suitcase in the coatroom. When the group wanted to leave, the coatroom attendant handed each person a coat and a suitcase in a random fashion. (a) In how many ways could the attendant return the coats and suitcases if nobody got his own coat back and nobody got his own suitcase back? (b) In how many ways could the attendant return the coats and suitcases if some people might have gotten one of their belong- ings back, but nobody got two of his belongings back?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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