(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

there are 30 red balls, 30 white balls, and 30 blue balls in a container. you draw 10 of them, without replacement. what is the probability that at least one color won't be selected.

2. Relevant equations

3. The attempt at a solution

i've been working on this one for too long. someone gave me a solution, but after i thought about it i realized it didn't work if you don't replace. the best solution i could come up with is the following:

for the total number of possibilities, since i can draw 90 for my first, 89 for my second and so on, i have 90!/80! ways of drawing balls.

for the number which exclude one color, i have 90*89 (and here i have to reduce the pool by 30 so those don't get selected)*58*57*...51.

but then someone pointed out that order doesn't matter, and i wasn't sure if there was something i could multiply this number by to make order irrelevant.

as always, i'm looking for hints more than a solution. also, variations on this problem would be cool too. i'm here to learn, people!

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# Homework Help: Probability: sampling without replacement

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