A basket contains only three kinds of fruits -guavas mangoes and pears .What is the minimum number of fruits that should be picked from the basket to ensure that at least 5 guavas or at least 7 mangoes or at least 8 pears are picked ?

Options

A. 20
B. 19
C. 17
D. 18

Answer

To solve the problem, we need to determine the minimum number of fruits that should be picked from the basket to ensure that we have at least 5 guavas, 7 mangoes, or 8 pears.

### Step-by-Step Solution:

1. **Identify the Conditions**: We need at least:
- 5 guavas
- 7 mangoes
- 8 pears

2. **Calculate the Maximum Undesired Outcomes**:
- To find the maximum number of fruits we can pick without satisfying any of the conditions, we can pick:
- 4 guavas (one less than 5)
- 6 mangoes (one less than 7)
- 7 pears (one less than 8)

3. **Sum the Maximum Undesired Fruits**:
- Total fruits picked without fulfilling any condition:
\[ 4 \text{ (guavas)} + 6 \text{ (mangoes)} + 7 \text{ (pears)} = 17 \text{ fruits} \]

4. **Determine the Minimum Number of Fruits to Ensure a Desired Outcome**:
- To ensure that we have at least one of the desired outcomes (5 guavas, 7 mangoes, or 8 pears), we need to pick one more fruit than the maximum undesired outcome:
\[ 17 + 1 = 18 \]

5. **Conclusion**:
- Therefore, the minimum number of fruits that should be picked from the basket to ensure that at least 5 guavas or at least 7 mangoes or at least 8 pears are picked is **18**.

### Final Answer:
The minimum number of fruits that should be picked is **18**.

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