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Problem from "Introduction to Probability" by Blitzstein-Hwang:

a) How many 7-digit phone numbers are possible assuming phone numbers can't start with 0 or 1.

b) Re-solve a) but now phone numbers can't start with 911 either.

The best I could come up with was:

a) 8 000 000 (8 x 10^6);

b) 5 670 000 (7 x 9^2 x 10^4);

Is this the right way of thinking about this problem?

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Your answer for (a) is correct, but for (b), you just need to subtract the number of phone numbers starting with 911. Number of such phone numbers is $10^4$ because once you set the leftmost part to 911, you can choose the other fours digits arbitrarily.

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  • $\begingroup$ Thank you, @gunes. I'd never have thought of that.... $\endgroup$
    – Reader 123
    Sep 7 '20 at 18:59

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