41-52 Counting Permutations These exercises involve counting permutations.
Running a Race In how many different ways can a race with nine runners be completed, assuming that there is no tie?
The number of different ways by which, the race of nine runners can be completed.
The total number of runners is nine and the condition is that there is no tie.
The number of permutations of distinct objects taken at a time is
There are total nine runners in a race and the number of different ways of completing the race of nine runners is similar to the number of different ways of selecting the nine runners at a time.
Thus, it is given as,
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