How many ways can 2 students be selected from a group of 5? (2019)

How many ways can 2 students be selected from a group of 5? (2019)

Step 1: Understand that we want to choose 2 students from a total of 5 students.
Step 2: Recognize that the order in which we select the students does not matter. This means we are using combinations, not permutations.
Step 3: Use the combination formula, which is written as nCr, where n is the total number of items (students) and r is the number of items to choose. Here, n = 5 and r = 2.
Step 4: The combination formula is nCr = n! / (r! * (n - r)!). In our case, it becomes 5C2 = 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: 5C2 = 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 select 2 students from a group of 5.

Combinatorics – The study of counting, specifically how to choose a subset of items from a larger set without regard to the order of selection.
Binomial Coefficient – The formula used to calculate the number of ways to choose k items from n items, denoted as nCk or C(n, k).