To determine the number of possible five-digit codes that start with an even number, we can break down the problem as follows:
-
Choosing the first digit (even number): The even digits are 0, 2, 4, 6, and 8. This gives us a total of 5 options for the first digit.
-
Choosing the remaining four digits: For each of the next four digits, Kami can use any digit from 0 to 9. That gives her 10 options for each of the remaining digits.
Now, we can calculate the total number of possible codes:
- For the first digit: 5 options (even digits: 0, 2, 4, 6, 8)
- For the second digit: 10 options (digits: 0-9)
- For the third digit: 10 options (digits: 0-9)
- For the fourth digit: 10 options (digits: 0-9)
- For the fifth digit: 10 options (digits: 0-9)
So, the total number of possible codes can be calculated as follows:
\[ \text{Total Codes} = (\text{choices for first digit}) \times (\text{choices for second digit}) \times (\text{choices for third digit}) \times (\text{choices for fourth digit}) \times (\text{choices for fifth digit}) \]
\[ \text{Total Codes} = 5 \times 10 \times 10 \times 10 \times 10 \]
Calculating this gives:
\[ 5 \times 10^4 = 5 \times 10000 = 50000 \]
Thus, Kami can create 50,000 codes that start with an even number.
The answer is 50,000 codes.