Difference between revisions of "1985 AJHSME Problems/Problem 22"
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Revision as of 17:07, 3 July 2013
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 ![\[\frac{1}{8}\cdot \frac{1}{10}=\frac{1}{80}\]](http://latex.artofproblemsolving.com/a/4/5/a456f704d11b2cb826e1964b6c0c52649681eb78.png)
See Also
| 1985 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 21 |
Followed by Problem 23 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
