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How many possible 10-digit phone numbers are possible (7 digits plus the
area code)? Type your answer into the box.

Respuesta :

Using the Fundamental Counting Theorem, it is found that 3,250,000,000 phone numbers are possible.

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:

  • For the first 3 digits, which correspond to the area code, there are 325 options in total, that is, [tex]n_1n_2n_3 = 325[/tex].
  • For the final 7 digits, each of them has 10 options.

Hence:

[tex]T = 325 \times 10^7 = 3,250,000,000[/tex]

3,250,000,000 phone numbers are possible.

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

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