There are 3 oranges, 5 apples and 6 mangoes in a fruit basket. Number of ways in which at least one fruit can be selected from the basket is

Options

A. 168
B. 167
C. 125
D. 124

Answer

To solve the problem of finding the number of ways to select at least one fruit from a basket containing 3 oranges, 5 apples, and 6 mangoes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Number of Fruits**:
- We have:
- 3 oranges
- 5 apples
- 6 mangoes

2. **Calculate the Number of Ways to Select Each Type of Fruit**:
- For oranges, since we can select 0 to 3 oranges, the number of ways to select oranges is \(3 + 1 = 4\) (0, 1, 2, or 3).
- For apples, since we can select 0 to 5 apples, the number of ways to select apples is \(5 + 1 = 6\) (0, 1, 2, 3, 4, or 5).
- For mangoes, since we can select 0 to 6 mangoes, the number of ways to select mangoes is \(6 + 1 = 7\) (0, 1, 2, 3, 4, 5, or 6).

3. **Calculate the Total Number of Ways to Select Fruits**:
- The total number of ways to select any combination of fruits (including selecting none) is given by multiplying the number of ways to select each type:
\[ \text{Total ways} = (3 + 1)(5 + 1)(6 + 1) = 4 \times 6 \times 7 \]

4. **Perform the Multiplication**:
- First, calculate \(4 \times 6 = 24\).
- Then calculate \(24 \times 7 = 168\).
- Therefore, the total number of ways to select fruits (including selecting none) is 168.

5. **Exclude the Case of Selecting No Fruits**:
- Since we want the number of ways to select at least one fruit, we need to subtract the one way in which no fruits are selected:
\[ \text{Ways to select at least one fruit} = 168 - 1 = 167 \]

### Final Answer:
The number of ways in which at least one fruit can be selected from the basket is **167**.