Using the Fundamental Counting Theorem, it is found that Kami could create 40,000 codes that start with an even number.
What is the Fundamental Counting Theorem?
It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
- The first digit has to be even, that is, 2, 4, 6 or 8, hence [tex]n_1 = 4[/tex].
- For the remaining digits there are 10 outcomes for each.
Hence:
[tex]N = 4 \times 10^4 = 40000[/tex]
Kami could create 40,000 codes that start with an even number.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
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