Question 10

Explanation

To determine the number of possible house numbers, we can use the multiplication rule (filling slots).

Step 1: Identifying Available Digits

The available digits are whole numbers less than $10$, which are $\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$.

From this set, we categorize them into:

• Odd Digits: $\{1, 3, 5, 7, 9\}$ (there are $5$ digits).
• Even Digits: $\{0, 2, 4, 6, 8\}$ (there are $5$ digits).

Step 2: Filling the Digit Positions

The house number consists of two digits with the following conditions:

1. First Digit (Odd): We must choose one of the $5$ available odd digits.
2. Second Digit (Even): We must choose one of the $5$ available even digits.

Step 3: Calculating Total Possibilities

The total number of ways to form the house number is the product of the choices for each position:

So, there are $25$ possible house numbers that can be formed.