Difference between revisions of "1999 AIME Problems/Problem 10"
m |
|||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| + | Ten points in the plane are given, with no three collinear. Four distinct segments joining pairs of these points are chosen at random, all such segments being equally likely. The probability that some three of the segments form a triangle whose vertices are among the ten given points is <math>\displaystyle m/n,</math> where <math>\displaystyle m_{}</math> and <math>\displaystyle n_{}</math> are relatively prime positive integers. Find <math>\displaystyle m+n.</math> | ||
== Solution == | == Solution == | ||
== See also == | == See also == | ||
| + | * [[1999_AIME_Problems/Problem_9|Previous Problem]] | ||
| + | * [[1999_AIME_Problems/Problem_11|Next Problem]] | ||
* [[1999 AIME Problems]] | * [[1999 AIME Problems]] | ||
Revision as of 01:59, 22 January 2007
Problem
Ten points in the plane are given, with no three collinear. Four distinct segments joining pairs of these points are chosen at random, all such segments being equally likely. The probability that some three of the segments form a triangle whose vertices are among the ten given points is 
where 
and 
are relatively prime positive integers. Find 
