Difference between revisions of "2000 AIME II Problems/Problem 5"

Revision as of 18:26, 11 November 2007

Problem

Given eight distinguishable rings, let $n$ be the number of possible five-ring arrangements on the four fingers (not the thumb) of one hand. The order of rings on each finger is significant, but it is not required that each finger have a ring. Find the leftmost three nonzero digits of $n$ .

Solution

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 == Problem ==
-Each of two boxes contains both black and white marbles, and the total number of marbles in the two boxes is <math>25.</math> One marble is taken out of each box randomly. The probability that both marbles are black is <math>27/50,</math> and the probability that both marbles are white is <math>m/n,</math> where <math>m</math> and <math>n</math> are relatively prime positive integers. What is <math>m + n</math>?
+Given eight distinguishable rings, let <math>n</math> be the number of possible five-ring arrangements on the four fingers (not the thumb) of one hand. The order of rings on each finger is significant, but it is not required that each finger have a ring. Find the leftmost three nonzero digits of <math>n</math>.
 == Solution ==

2000 AIME II (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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Difference between revisions of "2000 AIME II Problems/Problem 5"

Revision as of 18:26, 11 November 2007

Problem

Solution

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