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How do you find the possibilities in a 10-digit telephone number?


Would you believe someone who earned a 92% in grade eleven math forgot how to do this calculation? Pity me, please! How do you find this answer?

its 10 to the 10th power. 10x10x10x10x10x10x10x10x10x10=1000000000...

Assuming you take any combination of digits, you have 10 choices for the first digit, 10 choices for the 2nd, 10 choices for the 3rd, etc.

This works out to:
10 x 10 x 10 x 10 x... x 10 x 10 (ten times)

That is 10^10 or 10 billion combinations.

In reality, certain combinations aren't allowed. For example, the first digit can't be a 0 or 1. Starting digits like 911 and 411 are reserved and can't be an area code. But putting those exceptions aside, the answer is 10 billion combinations of 10 diigts.

If someone were to go through the North American Numbering Plan (search Wikipedia) and determine all the exceptions you'd get a smaller number, but I don't think you really were asking that.

It depends on whether the digits repeat or not:
If they can repeat the answer is 10^10
If they don't repeat the answer is 10! (10 x 9 x 8 x 7 x 6...)
I have a test on this stuff tomorrow so it's pretty fresh in my head haha!

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