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| Line 3: |
Line 3: |
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| | == Solution == | | == Solution == |
| − | Mutiplying each side by <math>19!</math>, We have <center><math>\binom{19}{2}+\binom{19}{3}+\binom{19}{4}+\binom{19}{5}+\binom{19}{6}+\binom{19}{7}+\binom{19}{8}+\binom{19}{9}=19N</math></center> Since we know that <center><math>\binom{19}{0}+\binom{19}{1}+...+\binom{19}{9}=\frac{1}{2}\cdot(2^{19})=2^{18}</math>
| + | |
| − | </center> Hence, we know that the above equation equates to
| |
| | == See also == | | == See also == |
| | {{AIME box|year=2000|n=II|num-b=6|num-a=8}} | | {{AIME box|year=2000|n=II|num-b=6|num-a=8}} |
Revision as of 07:17, 25 February 2008
Problem
Given that
find the greatest integer that is less than 
.
Solution
See also
.
