Difference between revisions of "2011 AIME II Problems/Problem 12"

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Nine delegates, three each from three different countries, randomly select chairs at a round table that seats nine people. Let the probability that each delegate sits next to at least one delegate from another country be m/n where m and n are relatively prime positive integers. Find m+n.
 
Nine delegates, three each from three different countries, randomly select chairs at a round table that seats nine people. Let the probability that each delegate sits next to at least one delegate from another country be m/n where m and n are relatively prime positive integers. Find m+n.
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Solution:
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Use complementary probability and PIE.

Revision as of 18:39, 31 March 2011

Problem:

Nine delegates, three each from three different countries, randomly select chairs at a round table that seats nine people. Let the probability that each delegate sits next to at least one delegate from another country be m/n where m and n are relatively prime positive integers. Find m+n.

Solution:

Use complementary probability and PIE.

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