Kami is in charge of creating a five-digit code to lock and unlock a secure chamber. She can use any digit from 0 through 9, and she can use each digit as many times as she wants. She knows she wants to start the code with an even number.

How many possible codes that start with an even number could Kami create?

Responses

40,000 codes
40,000 codes

50,000 codes
50,000 codes

400,000 codes
400,000 codes

500,000 codes

1 answer

To determine the number of possible five-digit codes that start with an even number, we can break down the problem as follows:

  1. 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.

  2. 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.