From a group of 8 people, how many ways can a team of 4 be selected?

From a group of 8 people, how many ways can a team of 4 be selected?

Step 1: Understand that we need to choose 4 people from a group of 8.
Step 2: Recognize that the order in which we choose the people does not matter (i.e., choosing person A, B, C, D is the same as choosing D, C, B, A).
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. Here, n = 8 and r = 4.
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 8C4 using the formula: 8C4 = 8! / (4! * (8 - 4)!) = 8! / (4! * 4!).
Step 6: Calculate the factorials: 8! = 40320, 4! = 24, so 4! * 4! = 24 * 24 = 576.
Step 7: Now, divide: 8C4 = 40320 / 576 = 70.
Step 8: Conclude that there are 70 different ways to select a team of 4 people 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 or C(n, r).