Question

use a permutation expression to solve.
in a race of 43 people, how many different ways can the runners place in 1st, 2nd, and 3rd?
12,341
24,682
74,046
79,507

Explanation:

Step1: Identify the permutation formula

The formula for permutations is \(P(n,r)=\frac{n!}{(n - r)!}\), where \(n\) is the total number of items, and \(r\) is the number of items to be selected and arranged. Here, \(n = 43\) and \(r=3\).

Step2: Substitute values into the formula

$$
LATEXBLOCK0
$$

Step3: Calculate the product

$$
LATEXBLOCK1
$$

Answer:

74,046 (the third option)