There are 9 pairs of white shoes and 6 pairs of black shoes contained in a box. We are allowed to draw only one shoe at a time. Minimum how many shoes are required to be drawn out to get one pair of white shoes?

Options

A. 11
B. 22
C. 33
D. 15

Answer

To solve the problem of determining the minimum number of shoes required to be drawn out in order to get one complete pair of white shoes, we can follow these steps:

### Step 1: Understand the total number of shoes
We have:
- 9 pairs of white shoes = 18 white shoes (9 left + 9 right)
- 6 pairs of black shoes = 12 black shoes (6 left + 6 right)

### Step 2: Consider the worst-case scenario
To ensure that we get at least one complete pair of white shoes, we need to consider the worst-case scenario where we draw the maximum number of shoes without completing a pair.

### Step 3: Draw black shoes first
In the worst-case scenario, we could draw all the black shoes first. Since there are 12 black shoes (6 left and 6 right), we could potentially draw all of these before we start drawing white shoes.

### Step 4: Draw one shoe of each type
After drawing all 12 black shoes, we need to draw at least one more shoe to ensure we get a white shoe. This means we can draw one left white shoe or one right white shoe.

### Step 5: Complete the pair
To complete the pair, we need to draw one more shoe of the opposite type (if we drew a left white shoe first, we need to draw a right white shoe, and vice versa).

### Step 6: Calculate the total
So, the total number of shoes drawn in the worst-case scenario would be:
- 12 (all black shoes) + 1 (one white shoe) + 1 (to complete the pair) = 14 shoes.

### Conclusion
Thus, the minimum number of shoes required to be drawn out to get one pair of white shoes is **14**.

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