Question

question 3
3 pts
there are 14 top cheese - makers competing for the first, second, and third prize in the world cheese awards competition in italy. how many different ways can three cheese - makers win the top three prizes?
note: your calculations may yield a large number. enter your answer in the box below without using comma in the number. the program will insert comma in the number where needed when you submit your answer.

Explanation:

Step1: Use permutation formula

The formula for permutations is \(P(n,r)=\frac{n!}{(n - r)!}\), where \(n = 14\) (total number of cheese - makers) and \(r=3\) (number of prizes).

Step2: Calculate factorial values

\(n!=14! = 14\times13\times12\times11!\) and \((n - r)!=(14 - 3)!=11!\). Then \(P(14,3)=\frac{14!}{11!}=14\times13\times12\).

Step3: Compute the product

\(14\times13 = 182\), and \(182\times12=2184\).

Answer:

2184