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.