How many ways can you select 2 students from a group of 8?

How many ways can you select 2 students from a group of 8?

Step 1: Understand that we want to choose 2 students from a total of 8 students.
Step 2: Recognize that the order in which we select 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, 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 = 8 and r = 2.
Step 4: The combination formula is nCr = n! / (r! * (n - r)!), where '!' denotes factorial (the product of all positive integers up to that number).
Step 5: Calculate 8C2 using the formula: 8C2 = 8! / (2! * (8 - 2)!)
Step 6: Simplify the calculation: 8! = 8 * 7 * 6!, 2! = 2 * 1 = 2, and (8 - 2)! = 6!. So, 8C2 = (8 * 7 * 6!) / (2 * 1 * 6!).
Step 7: The 6! cancels out, leaving us with 8C2 = (8 * 7) / (2 * 1).
Step 8: Calculate (8 * 7) = 56 and (2 * 1) = 2, so 8C2 = 56 / 2 = 28.
Step 9: Conclude that there are 28 different ways to select 2 students from a group of 8.

Combinatorics – The study of counting, arrangements, and combinations of objects.
Binomial Coefficient – The formula used to determine the number of ways to choose a subset of items from a larger set, denoted as nCr.