1999 AHSME Problems/Problem 24: Difference between revisions
New page: == Problem == Six points on a circle are given. Four of the chords joining pairs of the six points are selected at random. What is the probability that the four chords form a convex quadri... |
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{{AHSME box|year=1999|num-b=23|num-a=25}} | {{AHSME box|year=1999|num-b=23|num-a=25}} | ||
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Revision as of 13:35, 5 July 2013
Problem
Six points on a circle are given. Four of the chords joining pairs of the six points are selected at random. What is the probability that the four chords form a convex quadrilateral?
Solution
There are 
chords, and therefore 
ways how to choose four chords.
Each set of four points corresponds to exactly one convex quadrilateral, therefore there are 
cases in which the four chords form a convex quadrilateral.
The resulting probability is 
.
See also
| 1999 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 23 |
Followed by Problem 25 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
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