Suppose you are asked to list in order of preference the best three movies you've seen this year. If you saw eight movies this year, in how many ways can the three best be chosen and ranked?

Answer:

The three best can be chosen and ranked in 336 ways.

Step-by-step explanation:

Since you are asked to list the movies in order of preference, the order is important, as a higher order leads to a higher preference. This means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

If you saw eight movies this year, in how many ways can the three best be chosen and ranked?

[tex]P_{(8,3)} = \frac{8!}{(8-3)!} = 336[/tex]

The three best can be chosen and ranked in 336 ways.

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