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My state's lottery has 30 white balls numbered from 1 through 30 and 20 red balls numbered from 1 through 20. In each lottery drawing, 3 of the white balls and 2 of the red balls are drawn. To win, you must match all 3 white balls and both red balls, without regard to the order in which they were drawn. How many possible different combinations may be drawn?

 Sep 3, 2018

There are \(\dbinom{30}{3}\dbinom{20}{2} = 771400\) different combinations without regard to order

 Sep 5, 2018
edited by Rom  Sep 5, 2018

I think there is a minor typo in Rom's answer of (30C3 x 20C2) =771,400.

 Sep 5, 2018

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