How many ways can 3 different books be chosen from a set of 7 books?

How many ways can 3 different books be chosen from a set of 7 books?

Correct Answer: 35

Step 1: Understand that we want to choose 3 books from a total of 7 books.
Step 2: Recognize that the order in which we choose the books does not matter, so we will use combinations.
Step 3: The formula for combinations is given by nCr = 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 this case, n = 7 (total books) and r = 3 (books to choose).
Step 5: Plug the values into the formula: 7C3 = 7! / (3! * (7 - 3)!) = 7! / (3! * 4!).
Step 6: Calculate the factorials: 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1, 3! = 3 × 2 × 1, and 4! = 4 × 3 × 2 × 1.
Step 7: Simplify the expression: 7! = 5040, 3! = 6, and 4! = 24.
Step 8: Substitute the factorial values back into the equation: 7C3 = 5040 / (6 * 24).
Step 9: Calculate 6 * 24 = 144.
Step 10: Now divide 5040 by 144 to get the final answer: 5040 / 144 = 35.
Step 11: Therefore, there are 35 different ways to choose 3 books from a set of 7 books.

Combinations – The question tests the understanding of combinations, specifically how to choose a subset of items from a larger set without regard to the order of selection.