Difference between revisions of "2016 AMC 12A Problems/Problem 1"
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==Solution== | ==Solution== | ||
<cmath>\frac{11!-10!}{9!} = \frac{11!}{9!} - \frac{10!}{9!}</cmath> | <cmath>\frac{11!-10!}{9!} = \frac{11!}{9!} - \frac{10!}{9!}</cmath> | ||
| − | <cmath>\frac{11\cdot 10\cdot 9!}{9!} - \frac{10\cdot 9!}{9!}</cmath> | + | <cmath>=\frac{11\cdot 10\cdot 9!}{9!} - \frac{10\cdot 9!}{9!}</cmath> |
| − | <cmath>(11\cdot 10) - 10</cmath> | + | <cmath>=(11\cdot 10) - 10</cmath> |
<cmath>\boxed{\textbf{(B) } \, 100}</cmath> | <cmath>\boxed{\textbf{(B) } \, 100}</cmath> | ||
Revision as of 22:05, 3 February 2016
Problem
What is the value of 
?
Solution
![\[\frac{11!-10!}{9!} = \frac{11!}{9!} - \frac{10!}{9!}\]](http://latex.artofproblemsolving.com/4/b/7/4b7f9aefc4bc405d52960b5bf8683575f9b88127.png)
![\[=\frac{11\cdot 10\cdot 9!}{9!} - \frac{10\cdot 9!}{9!}\]](http://latex.artofproblemsolving.com/0/6/c/06c33a457fb264b102388e5420bf3962c8b0dd0c.png)
![\[=(11\cdot 10) - 10\]](http://latex.artofproblemsolving.com/4/8/b/48bd8fa98d4d1fc2acbce3ff1d085ccad639ec6f.png)
![\[\boxed{\textbf{(B) } \, 100}\]](http://latex.artofproblemsolving.com/1/a/7/1a747c98711cdc6dbda95d3a326207d3bbb64bb6.png)
See Also
| 2016 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by First Problem |
Followed by Problem 2 |
| 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 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
