How many ways can 3 different fruits be chosen from 8 fruits?

How many ways can 3 different fruits be chosen from 8 fruits?

Correct Answer: 56

Step 1: Understand that we need to choose 3 different fruits from a total of 8 fruits.
Step 2: Recognize that the order in which we choose the fruits 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 (the total fruits) and r = 3 (the fruits we want to choose).
Step 5: Plug the values into the formula: C(8, 3) = 8! / (3! * (8 - 3)!)
Step 6: Calculate 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, but we can simplify it for our calculation.
Step 7: Calculate 3! = 3 × 2 × 1 = 6.
Step 8: Calculate (8 - 3)! = 5! = 5 × 4 × 3 × 2 × 1.
Step 9: Now simplify C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1) = 336 / 6 = 56.
Step 10: Therefore, the number of ways to choose 3 different fruits from 8 fruits is 56.

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.