Question

select the correct answer from each drop - down menu. the state swim meet has 27 swimmers competing for first through fourth place in the 100 - meter butterfly race. complete the statement describing this situation. this is an example of a ☐. there are ☐ possible arrangements of first through fourth place winners. (the drop - down for the first blank has options combination and permutation; there are also reset and next buttons.)

Explanation:

Step1: Identify arrangement type

Since the order (1st, 2nd, 3rd, 4th place) matters, this is a permutation.

Step2: Apply permutation formula

We calculate permutations of 27 swimmers taken 4 at a time, using the formula $P(n,k)=\frac{n!}{(n-k)!}$ where $n=27$, $k=4$.
$$P(27,4)=\frac{27!}{(27-4)!}=27\times26\times25\times24$$

Step3: Compute the product

$$27\times26=702$$
$$702\times25=17550$$
$$17550\times24=421200$$

Answer:

This is an example of a permutation. There are 421200 possible arrangements of first through fourth place winners.