5

Part of 2000 AIME Problems

Problems(2)

Black and White Marbles

Source:

Each of two boxes contains both black and white marbles, and the total number of marbles in the two boxes is

25.

One marble is taken out of each box randomly. The probability that both marbles are black is

27/50,

and the probability that both marbles are white is

m/n,

m

n

are relatively prime positive integers. What is

m+n?

probabilitynumber theoryrelatively prime

Ring Arrangements

Source:

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.

countingdistinguishabilityfunctionLaTeX