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?

Answer 1

Answer: There are 504 ways in which first, second, and third place can be assigned.

Explanation:

Since we have given that

Number of students in the computer club = 9

Number of students are getting prizes for first, second, third = 3

We need to find the number of ways in which first, second, third place can be assigned .

So, we will use "Permutation" as we need an arrangement:

i.e.

$^nP_r=\frac{n!}{(n-r)!}$

where, n is the number of total students and

r is the number of people in a group.

So,

$^9P_3=\frac{9!}{(9-3)!}\\\\^9P_3=\frac{9!}{6!}\\\\^9P_3=504$

Hence, there are 504 ways in which first, second, and third place can be assigned.

Answer 2

This solution is related to the mathematical concept of Permutation and there are 504 ways in which the prizes can be assigned.

What is Permutation?

Permutation in mathematics refers to the various options in which an order can take place. It is a linear order of a set of items and the many ways in which they can be arranged.

In order to solve the problem, we must use the formula for permutation.

The formula for permutation is given as:

P(n,r) = n! / (n-r)!

Where n refers to the number of total students and r is the number of people in the group.

This gives us:

P (9,3) = 9!/(9-3)!

P (9,3) = 9!/6!

P (9,3) = 504.

Learn more about Permutation at:
https://brainly.com/question/1216161