1985 AJHSME Problems/Problem 22
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Problem
Assume every 7-digit whole number is a possible telephone number except those that begin with or
. What fraction of telephone numbers begin with
and end with
?
Note: All telephone numbers are 7-digit whole numbers.
Solution
An equivalent problem is finding the probability that a randomly selected telephone number begins with and ends with
.
There are possibilities for the first digit in total, and only
that works, so the probability the number begins with
is
There are possibilities for the last digit, and only
that works
, so the probability the number ends with
is
Since these are independent events, the probability both happens is