From a set of 8 different books, how many ways can you choose 3 books?

From a set of 8 different books, how many ways can you choose 3 books?

Step 1: Understand that you have 8 different books.
Step 2: You want to choose 3 books from these 8 books.
Step 3: Recognize that the order in which you choose the books does not matter (choosing Book A, Book B, and Book C is the same as choosing Book C, Book A, and Book B).
Step 4: Use the combination formula, which is written as nCr, where n is the total number of items (books) and r is the number of items to choose. Here, n = 8 and r = 3.
Step 5: The combination formula is nCr = n! / (r! * (n - r)!), where '!' denotes factorial (the product of all positive integers up to that number).
Step 6: Calculate 8C3 using the formula: 8C3 = 8! / (3! * (8 - 3)!) = 8! / (3! * 5!).
Step 7: Calculate the factorials: 8! = 40320, 3! = 6, and 5! = 120.
Step 8: Substitute the factorials into the formula: 8C3 = 40320 / (6 * 120).
Step 9: Calculate the denominator: 6 * 120 = 720.
Step 10: Now divide: 40320 / 720 = 56.
Step 11: Conclude that there are 56 different ways to choose 3 books from 8.

Combinatorics – The study of counting, specifically how to choose 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.