From 5 oranges, 4 mangoes, and 3 bananas, one fruit of each type is to be chosen. In how many distinct selections can this be done?

Introduction / Context:We perform independent choices from disjoint categories (oranges, mangoes, bananas). The total number of selections is the product of independent counts.

Given Data / Assumptions:

• Oranges = 5, Mangoes = 4, Bananas = 3.
• Choose exactly one from each category.

Concept / Approach:Use the multiplication principle across independent categories: total ways = 5 * 4 * 3.

Step-by-Step Solution:5 * 4 * 3 = 60.

Verification / Alternative check:Enumerating choices per category confirms the product.

Why Other Options Are Wrong:120 doubles the count (perhaps ordering); 110 and 75 are unrelated combinations.

Common Pitfalls:Confusing selection (unordered) with arrangement (ordered) across categories.

Final Answer:60