From a group of 8 people, how many ways can a team of 3 be selected? (2022)

From a group of 8 people, how many ways can a team of 3 be selected? (2022)

Step 1: Understand that we need to choose 3 people from a group of 8.
Step 2: Recognize that this is a combination problem because the order of selection does not matter.
Step 3: Use the combination formula, which is written as nCr, where n is the total number of people and r is the number of people to choose. The formula is nCr = n! / (r! * (n - r)!).
Step 4: In our case, n = 8 and r = 3. So we will calculate 8C3.
Step 5: Plug the values into the formula: 8C3 = 8! / (3! * (8 - 3)!).
Step 6: Simplify the equation: 8C3 = 8! / (3! * 5!).
Step 7: Calculate 8! = 8 × 7 × 6 × 5! (we can cancel 5! in the numerator and denominator).
Step 8: Now we have 8C3 = (8 × 7 × 6) / (3 × 2 × 1).
Step 9: Calculate the numerator: 8 × 7 × 6 = 336.
Step 10: Calculate the denominator: 3 × 2 × 1 = 6.
Step 11: Divide the numerator by the denominator: 336 / 6 = 56.
Step 12: Therefore, the number of ways to choose 3 people from 8 is 56.

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.