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# counting question

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Assume every 7-digit whole number is a possible telephone number except those that begin with 0 or 1. What fraction of telephone numbers begin with 9 and end with 0?

mathtoo  Jun 3, 2018
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We have 7 slots for our options because there are 7 digits.

_ _ _ _ _ _ _ and the problem says that the telephone number cannot start with 0 or 1, we have:

8*10*10*10*10*10*10=8*10^6=8,000,000

8 digits for the first slot, excluding 0 or 1.

Now, the problem is asking us to find the fraction of telephone numbers begin with 9 and end with 0.

So, we have 1*10*10*10*10*10*1=1*10^5=100,000.

Thus, the fraction is: $$\frac{100000}{8000000}=\boxed{\frac{1}{80}}$$

tertre  Jun 3, 2018