Difference between revisions of "2005 AMC 12A Problems/Problem 23"
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[[Category:Introductory Combinatorics Problems]] | [[Category:Introductory Combinatorics Problems]] |
Revision as of 15:17, 9 September 2007
Problem
Two distinct numbers a and b are chosen randomly from the set . What is the probability that is an integer?
Solution
Let , so . Define , ; then , so . Here we can just make a table and count the number of values of per value of . The largest possible value of is 12, and we get .
The total number of ways to pick two distinct numbers is , so we get a probability of .
See also
2005 AMC 12A (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 12 Problems and Solutions |