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The counting principle states that if event 1 can take place in a number of ways and event 2 can take place in b number of ways, the number of ways in which event 1 and event 2 can take place is a*b. The number of ways in which r objects can be chosen from a set of n objects is the number of combinations C(n, r). Here, the order in which the objects are chosen is not important. If r objects are being chosen from a set of n objects and the order in which they are chosen is relevant, the number of ways in which this can be done is the number of permutations P(n, r). The factorial of a number is the product of all integers smaller than it starting with 1.
When six friends go to a movie and have to sit in a row of six seats, the order in which they sit is relevant. The number of ways in which this can be done is the number of permutations.
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