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

Line 2: | Line 2: | ||

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. | ||

+ | |||

+ | Solution: | ||

+ | |||

+ | 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.