How many 6-digit numbers have at least 1 even digit?

Options

A. 884375
B. 3600
C. 880775
D. 15624

Answer

To solve the problem of how many 6-digit numbers have at least one even digit, we can follow these steps:

### Step 1: Calculate the total number of 6-digit numbers
A 6-digit number cannot start with 0. Therefore, the first digit can be any digit from 1 to 9 (9 options). The remaining 5 digits can be any digit from 0 to 9 (10 options each).

So, the total number of 6-digit numbers is calculated as follows:
\[ \text{Total 6-digit numbers} = 9 \times 10^5 = 900000 \]

### Step 2: Calculate the number of 6-digit numbers with all odd digits
The odd digits are 1, 3, 5, 7, and 9 (5 options). Since we want all 6 digits to be odd, we can choose any of the 5 odd digits for each of the 6 positions.

Thus, the total number of 6-digit numbers with all odd digits is:
\[ \text{Total odd digit numbers} = 5^6 = 15625 \]

### Step 3: Calculate the number of 6-digit numbers with at least one even digit
To find the number of 6-digit numbers with at least one even digit, we can subtract the number of 6-digit numbers with all odd digits from the total number of 6-digit numbers.

So, we have:
\[ \text{Total with at least one even digit} = \text{Total 6-digit numbers} - \text{Total odd digit numbers} \]
\[ = 900000 - 15625 = 884375 \]

### Final Answer
Thus, the number of 6-digit numbers that have at least one even digit is **884375**.

---