Question

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?


40,000 codes

50,000 codes

400,000 codes

500,000 codes

Answer 1

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 $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

In this problem:

• The first digit has to be even, that is, 2, 4, 6 or 8, hence $n_1 = 4$.

• For the remaining digits there are 10 outcomes for each.

Hence:

$N = 4 \times 10^4 = 40000$

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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