Question

From a group of 10 students, we want to select a random sample of 5 students to serve on a university committee. How many combinations of random samples of 5 students can be selected?

Answer 1

There are 252 different combinations of 5 students that can be chosen from a group of 10 students to serve on a university committee. This is calculated using the combinations formula C(n, k) = n! / (k!(n-k)!), substituting n=10 and k=5.

Step-by-step explanation:

To determine the number of combinations of random samples of 5 students that can be selected from a group of 10 students, you use the combinations formula which is given by:

C(n, k) = n! / (k!(n-k)!)

Where:

• n is the total number of items,
• k is the number of items to choose,
• ! stands for factorial, meaning you multiply the number by all of the positive integers less than it.

In this case, n is 10 (the total number of students) and k is 5 (the number of students to select for the committee). Substitute these values into the formula to get:

C(10, 5) = 10! / (5! * (10-5)!) = 252

There are 252 different combinations of 5 students that can be formed from a group of 10 students.