Question

To create an entry​ code, you must first choose 3 letters and​ then, 6 ​single-digit numbers. How many different entry codes can you​ create?

Answer 1

Answer:

17576000000

Step-by-step explanation:

26 x 26 x 10 x 10 x 10 x 10 x 10 x 10

Answer 2

Using the Fundamental Counting Theorem, it is found that you can create 17,576,000,000 different entry codes.

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, for each letter there are 26 possible outcomes and for each digit there are 10 possible outcoms, hence:

$N = 26^3 \times 10^6 = 17,576,000,000$

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

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