Question

select the correct answer from each drop - down menu.
a cross country race has 45 runners competing for first through fourth place.
complete the statement describing this situation.
this is an example of a
permutation
combination
. there are possible arrangements of first through fourth place winners.
reset next

Explanation:

Step1: Identify permutation/combination

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

Step2: Apply permutation formula

The formula for permutations is $P(n,k)=\frac{n!}{(n-k)!}$, where $n=45$ (total runners), $k=4$ (places to fill).

Step3: Calculate factorial values

$$\begin{align*} P(45,4)&=\frac{45!}{(45-4)!}\\ &=45\times44\times43\times42\\ &=3575880 \end{align*}$$

Answer:

1. permutation
2. 3,575,880