three out of nine students in the computer club are getting prizes for first, second, and third place in a…

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

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

Answer

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")