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My wife and I cannot figure out how to do a probability question including an "at most" clause. We are given 18 items, 10 of a and 8 of b. If we pick three at random, we need to know how many possibilities of three have at most 2 of b.

We tried finding the probability of having exactly 0 and 1 of b but we can't figure out how to invert it (which is what the internet suggested).

I've tried googling it and only got binomial probability which is far more complicated than her intro to math class.

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If you can have at most 2 b's, that means the only case that wouldn't count is if all 3 were b's. So, if you can find that probability, you can subtract that from 1 to get the probability of not all 3 being b's, which is equivalent to at most 2 of them being b's.

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