Difference between revisions of "2010 AMC 10B Problems/Problem 23"
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==Solution== | ==Solution== | ||
| − | + | By the [http://en.wikipedia.org/wiki/Young_tableau#Dimension_of_a_representation hook-length formula], the answer is <math> \frac{9!}{5\cdot 4^{2}\cdot 3^{3}\cdot 2^{2}\cdot 1}= \boxed{\textbf{(D)}\ 42}</math> | |
| − | By the [http://en.wikipedia.org/wiki/Young_tableau#Dimension_of_a_representation hook-length formula], the answer is <math> \frac{9!}{5\cdot 4^{2}\cdot 3^{3}\cdot 2^{2}\cdot 1}= | ||
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== See also == | == See also == | ||
{{AMC10 box|year=2010|ab=B|num-b=22|num-a=24}} | {{AMC10 box|year=2010|ab=B|num-b=22|num-a=24}} | ||
Revision as of 15:41, 26 November 2011
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 | ||
