Difference between revisions of "2005 AMC 10B Problems/Problem 20"
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Revision as of 11:15, 4 July 2013
Problem
What is the average (mean) of all -digit numbers that can be formed by using each of the digits 1, 3, 5, 7, 8 and exactly once?
Solution
We first look at how many times each number will appear in each slot. If we fix a number in a slot, then there are 
ways to arrange the other numbers, so each number appears in each spot 
times. Therefore, the sum of all such numbers is 
Since there are 
such numbers, we divide 
to get 
See Also
| 2005 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 19 |
Followed by Problem 21 | |
| 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 AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
