Card type problem, 3 draws

I read the sticky and watched some videos and learned a bit about some basic statistics concepts.

I am struggling with the following problem:

You have a stack of 10 cards.
7 are black 3 are red
If you draw 3 cards from the same pool of 10, what is the probability that at least 1 will be red?

Thanks for any help.

Quote:

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Originally Posted by hardwarefailure

You have a stack of 10 cards.
7 are black 3 are red
If you draw 3 cards from the same pool of 10, what is the probability that at least 1 will be red?

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It is 1 minus the probability that none of the three is red.

Quote:

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Originally Posted by Plato

It is 1 minus the probability that none of the three is red.

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And what is the probability that none of the 3 are red?

Is that (7/10)*(6/9)*(5/7)?

If so the probability of said problem is .666 or 2/3?

Thanks again.