Question

in how many different orders can 16 horses in the kentucky derby finish in the top four spots if there are no ties? question help: video ebook written example

Explanation:

Step1: Identify the problem type

This is a permutation problem where we want to find the number of ways to arrange 16 horses in the top 4 spots. The formula for permutations is \( P(n, r)=\frac{n!}{(n - r)!} \), where \( n = 16 \) (total number of horses) and \( r=4 \) (number of spots to fill).

Step2: Apply the permutation formula

Substitute \( n = 16 \) and \( r = 4 \) into the formula:

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Step3: Calculate the product

Calculate \( 16\times15 = 240 \), \( 240\times14=3360 \), \( 3360\times13 = 43680 \).

Answer:

43680