A bag contians balls of two colours, 3 black and 3 white. What is the smallsest number of balls which must be drawn from the bag, without looking, so that the among these three are two of the same colour?

Options

A. 2
B. 3
C. 4
D. 5

Explanation

To solve the problem of finding the smallest number of balls that must be drawn from a bag containing 3 black and 3 white balls, such that at least two of the drawn balls are of the same color, we can use the Pigeonhole Principle.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have a bag with 3 black balls and 3 white balls. We need to determine how many balls we must draw to ensure that at least two of them are of the same color.

2. **Applying the Pigeonhole Principle**:
The Pigeonhole Principle states that if you have more items than containers, at least one container must contain more than one item. In our case, the "containers" are the colors of the balls (black and white).

3. **Identifying the Colors**:
There are two colors of balls: black and white.

4. **Drawing Balls**:
If we draw 1 ball, it could be either black or white. If we draw 2 balls, we could have one of each color (1 black and 1 white).

5. **Drawing a Third Ball**:
When we draw a third ball, regardless of the color, we will have at least two balls of the same color. This is because we only have two colors to choose from.

6. **Conclusion**:
Therefore, to guarantee that at least two balls are of the same color, we must draw a minimum of 3 balls.

### Final Answer:
The smallest number of balls that must be drawn from the bag to ensure that at least two of them are of the same color is **3**.

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