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Find the rainbow (Posted on 2019-06-13) Difficulty: 3 of 5
Seven balls of different weights are randomly painted red, orange, yellow, green, blue, indigo and violet, each ball being painted a distinct color.

The green ball is found to be heavier than the blue ball, and the red ball is found to be heavier than the yellow ball.

What is the probability that the red ball is heavier than the blue ball?

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution Solution Comment 1 of 1
Since the orange, indigo, and violet balls were never weighed or considered.  We can pretend they never existed.  

Of the four remaining, there were 4!=24 possible orderings, but the given g>b and r>y reduces this to 24/2/2=6.  

These are easy enough to list:

rygb *
rgyb *
rgby *
gryb *
grby *
gbry

The probability is 5/6.


  Posted by Jer on 2019-06-13 10:37:46
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