How many ways can 2 out of 5 students be selected?

How many ways can 2 out of 5 students be selected?

Step 1: Understand that we want to choose 2 students from a group of 5 students.
Step 2: Recognize that the order in which we choose the students does not matter (choosing Student A and then Student B is the same as choosing Student B and then Student A).
Step 3: Use the combination formula C(n, r) = n! / (r! * (n - r)!), where n is the total number of students (5) and r is the number of students to choose (2).
Step 4: Plug in the values into the formula: C(5, 2) = 5! / (2! * (5 - 2)!).
Step 5: Calculate 5! (which is 5 x 4 x 3 x 2 x 1 = 120), 2! (which is 2 x 1 = 2), and (5 - 2)! (which is 3! = 3 x 2 x 1 = 6).
Step 6: Substitute these values into the formula: C(5, 2) = 120 / (2 * 6).
Step 7: Calculate the denominator: 2 * 6 = 12.
Step 8: Now divide: 120 / 12 = 10.
Step 9: Conclude that there are 10 different ways to choose 2 students from 5.

Combinatorics – The study of counting, arrangements, and combinations of objects.
Binomial Coefficient – The formula C(n, k) = n! / (k!(n-k)!) used to calculate the number of ways to choose k elements from a set of n elements.