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Three different types of objects in a bucket. How many times does one need to select object from the bucket to get atleast 3 objects of the same type?
    Correct answer is '7'. Can you explain this answer?
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    Three different types of objects in a bucket. How many times does one ...
    Explanation:

    To solve this problem, we will use the Pigeonhole Principle. According to this principle, if there are n pigeonholes and n+1 pigeons, then there must be at least one pigeonhole with more than one pigeon.

    Step 1:

    We have three different types of objects in a bucket. Let's consider these objects as pigeonholes.

    Step 2:

    We need to select objects from the bucket until we get at least 3 objects of the same type. Let's consider these selections as pigeons.

    Step 3:

    To ensure that we get at least 3 objects of the same type, we need to select at least 3 pigeons for each pigeonhole. Therefore, we need to select a minimum of 3 x 3 = 9 pigeons.

    Step 4:

    However, we only have 3 different types of objects, which means we only have 3 pigeonholes. Therefore, we cannot select 9 pigeons without selecting at least 3 pigeons of the same type.

    Step 5:

    Therefore, the minimum number of selections required to get at least 3 objects of the same type is 7. This is because if we select any 6 objects, we could end up with 2 objects of each type, but if we select the 7th object, we are guaranteed to have at least 3 objects of one type.

    Therefore, the correct answer is 7.
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