Question

there are 16 finalists in a singing competition. the top six singers receive prizes. how many ways can the singers finish first through sixth?

there are different ways that the singers can finish first through sixth.
(type a whole number.)

Explanation:

Identify the parameters

We have a total of \(n = 16\) finalists. We want to find the number of ways they can finish in the top six positions (first through sixth), so we are selecting \(r = 6\) singers.

Determine if order matters

Using the Permutations vs Combinations knowledge point

$$ \text{Since finishing order (1st, 2nd, ..., 6th) is distinct, order matters. We use permutations: } P(n, r) = \frac{n!}{(n-r)!} $$

Calculate the permutations

Using the Permutations vs Combinations knowledge point

$$
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Answer:

There are <blank>5,765,760</blank> different ways that the singers can finish first through sixth.