Question

three out of nine students in the computer club are getting prizes for first, second, and third place in a competition.
how many ways can first, second, and third place be assigned?
$_{9}p_{3}=\frac{9!}{(9-3)!}$
○ 3
○ 84
○ 504
○ 2048

Explanation:

Step1: Recall permutation formula

The permutation formula is $_nP_r = \frac{n!}{(n-r)!}$, where $n=9$, $r=3$.

Step2: Substitute values into formula

$$_9P_3 = \frac{9!}{(9-3)!} = \frac{9!}{6!}$$

Step3: Simplify factorial expression

$9! = 9\times8\times7\times6!$, so $\frac{9\times8\times7\times6!}{6!} = 9\times8\times7$

Step4: Calculate the product

$9\times8\times7 = 504$

Answer:

504 (the correct option is the one labeled "504")