What's wrong with my logic on this combinatorial/probability question?

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SUMMARY

The discussion focuses on solving a combinatorial probability problem involving the selection of blue and red balls. The participant identifies that at least 3 out of 9 distinguishable blue balls must be selected, leading to 5 specific combinations of blue and red balls. The key error in the initial logic is the failure to account for the total number of distinguishable blue balls available. The correct approach involves using combinations to determine the number of ways to select 3 blue balls from the total of 9.

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Homework Statement



prob.png


The Attempt at a Solution



If at least 3 balls must be blue, then the possible ways of selecting at least 3 blues are:

r, b, b, b
b, r, b, b
b, b, r, b
b, b, b, r
b, b, b, b

where r = red ball, and b = blue ball

So there are 5 ways to draw 3+ blue.
 
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The question didn't really spell out what 'different' means. I think they want you to treat the balls as distinguishable and probably are not concerned with the order.
 
The problem with your logic is that there are 9 different blue balls and you don't account for all of them being possibly drawn.

My hint for you is to consider combinations, i.e. how many ways are there to choose 3 blue balls out of 9?
 

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