There are 4 Oranges, 4 apples and 6 mangoes in a fruit basket. In how many ways can a person make a selection of one or more fruits from among the fruits in the basket if all the fruits of the same type are different?

To determine how many ways a person can select one or more fruits from a basket containing 4 oranges, 4 apples, and 6 mangoes, we can use the concept of combinations.

Understanding the Selection Process

Since all fruits of the same type are considered different, we can treat each fruit as a unique item. Here's how to calculate the total selections:

Calculating Selections for Each Fruit Type

• For oranges: There are 4 different oranges. The selection options are 0 (not selecting any) to 4 (selecting all), giving us 5 choices (0, 1, 2, 3, or 4 oranges).
• For apples: Similarly, there are 4 different apples, providing another 5 choices.
• For mangoes: With 6 different mangoes, there are 7 choices (0 to 6 mangoes).

Total Combinations

To find the total number of ways to select fruits, we multiply the number of choices for each type:

Total selections = (Choices for oranges) × (Choices for apples) × (Choices for mangoes)

Total selections = 5 × 5 × 7 = 175

Excluding the Empty Selection

Since we want at least one fruit, we need to subtract the one case where no fruit is selected:

Final total = 175 - 1 = 174

Thus, there are 174 different ways to select one or more fruits from the basket.