Question

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?

Answer 1

The three whites:

(30 choose 1) * (29 choose 1) * (28 choose 1) = 30 * 29 * 28

The two reds:

(20 choose 1) * (19 choose 1) = 20 * 19

So, The three whites + two reds = 30 * 29 * 28 + 20 * 19 = 24740