How many ways can 2 students be selected from a group of 8? (2015)

How many ways can 2 students be selected from a group of 8? (2015)

Step 1: Understand that we want to select 2 students from a total of 8 students.
Step 2: Recognize that the order in which we select the students does not matter. This means we will use combinations, not permutations.
Step 3: The formula for combinations is C(n, r) = n! / (r! * (n - r)!), where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.
Step 4: In our case, n = 8 (total students) and r = 2 (students to select).
Step 5: Plug the values into the formula: C(8, 2) = 8! / (2! * (8 - 2)!)
Step 6: Calculate 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, but we can simplify it for our calculation.
Step 7: Calculate 2! = 2 × 1 = 2.
Step 8: Calculate (8 - 2)! = 6! = 6 × 5 × 4 × 3 × 2 × 1, but we can also simplify this.
Step 9: Simplifying C(8, 2) gives us: C(8, 2) = (8 × 7) / (2 × 1) = 56 / 2 = 28.
Step 10: Therefore, the number of ways to select 2 students from a group of 8 is 28.

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