12
Part of 2011 AIME Problems
Problems(2)
Some Men, Many Women
Source:
3/18/2011
Six men and some number of women stand in a line in random order. Let be the probability that a group of at least four men stand together in the line, given that every man stands next to at least one other man. Find the least number of women in the line such that does not exceed 1 percent.
probabilitycountingdistinguishabilityratioAMC
Delegates around table [2011.II.12]
Source:
3/31/2011
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 , where and are relatively prime positive integers. Find .
probabilitygeometrygeometric transformationrotationnumber theoryrelatively primecomplementary counting