![]() The number of permutations of \(n\) distinct objects can always be found by \(n!\).įinding the Number of Permutations of n Distinct Objects Using a Formulaįor some permutation problems, it is inconvenient to use the Multiplication Principle because there are so many numbers to multiply. Note that in part c, we found there were \(9!\) ways for \(9\) people to line up. There are \(362,880\) possible permutations for the swimmers to line up. There are \(9\) choices for the first spot, then \(8\) for the second, \(7\) for the third, \(6\) for the fourth, and so on until only \(1\) person remains for the last spot. Draw lines for describing each place in the photo.Multiply to find that there are \(56\) ways for the swimmers to place if Ariel wins first. There are \(8\) remaining options for second place, and then \(7\) remaining options for third place. We know Ariel must win first place, so there is only \(1\) option for first place. Multiply to find that there are \(504\) ways for the swimmers to place. ![]() Once first and second place have been won, there are \(7\) remaining options for third place. Once someone has won first place, there are \(8\) remaining options for second place. ![]()
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