How many different ways can 2 out of 5 different fruits be chosen?

How many different ways can 2 out of 5 different fruits be chosen?

Step 1: Understand that we have 5 different fruits.
Step 2: We want to choose 2 fruits from these 5.
Step 3: Recognize that the order in which we choose the fruits does not matter (choosing apple and banana is the same as choosing banana and apple).
Step 4: Use the combination formula C(n, r) = n! / (r! * (n - r)!), where n is the total number of items (fruits) and r is the number of items to choose.
Step 5: In our case, n = 5 (fruits) and r = 2 (fruits to choose).
Step 6: Calculate C(5, 2) using the formula: C(5, 2) = 5! / (2! * (5 - 2)!)
Step 7: Simplify the factorials: 5! = 5 × 4 × 3 × 2 × 1, 2! = 2 × 1, and (5 - 2)! = 3! = 3 × 2 × 1.
Step 8: Substitute the values into the formula: C(5, 2) = (5 × 4) / (2 × 1) = 20 / 2 = 10.
Step 9: Conclude that there are 10 different ways to choose 2 fruits from 5.

Combinations – The concept of combinations is used to determine the number of ways to choose a subset of items from a larger set, where the order of selection does not matter.