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In a competition of 18 runners, how many ways can you pick the best 3 runners if you have to pick the exact order they place?

Answer :

Final answer:

The number of ways to pick the best 3 runners out of 18 when the order is essential can be determined using the formula for permutations. Accordingly, the answer is 18! / (18-3)!, where '!' symbolizes a factorial.

Explanation:

In this scenario, we are dealing with a permutation problem, as the order of the selected objects (in this case, the runners) matters. Specifically, we want to determine the number of ways to arrange 3 runners in order out of a total of 18. In mathematics, the formula for permutations is defined as P(n, r) = n! / (n-r)!, where 'n' is the total number of options, 'r' is the number of options chosen, and '!' denotes a factorial, meaning the product of all positive integers up to that number.Therefore, in this case, n is 18 (the total number of runners), and r is 3 (the number of runners we are selecting). Thus, the number of permutations is P(18, 3) = 18! / (18-3)!. Calculation of these factorials and their division yields the number of different ways the top 3 runners can be selected in order.


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