Difference between revisions of "2010 AMC 10B Problems/Problem 23"
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The entries in a <math>3 \times 3</math> array include all the digits from 1 through 9, arranged so that the entries in every row and column are in increasing order. How many such arrays are there? | The entries in a <math>3 \times 3</math> array include all the digits from 1 through 9, arranged so that the entries in every row and column are in increasing order. How many such arrays are there? | ||
| − | <math> \textbf{(A)}\ 18\qquad\textbf{(B)}\ 24\ | + | <math> \textbf{(A)}\ 18\qquad\textbf{(B)}\ 24 \qquad\textbf{(C)}\ 36\qquad\textbf{(D)}\ 42\qquad\textbf{(E)}\ 60 </math> |
==Solution== | ==Solution== | ||
Revision as of 15:01, 21 August 2013
Problem
The entries in a 
array include all the digits from 1 through 9, arranged so that the entries in every row and column are in increasing order. How many such arrays are there?
Solution
By the hook-length formula, the answer is 
See also
| 2010 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 22 |
Followed by Problem 24 | |
| 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. 
