An urn contains 5 red, 4 white, and 3 blue numbered balls. We draw 3 together at random, with no order on the drawn balls.

i) How many possible outcomes are there?

ii) How many outcomes have one ball of each color?

iii) How many outcomes have at least 2 balls of the same color?

iv) If the drawing is uniformly random, about what percent of the time will we get at least 2 white balls?

i) 12 choose 3 = 220

ii) (5 choose 1)*(4 choose 1)*(3 choose 1) = 5*4*3 = 60

iii) (5 choose 2)+(5 choose 3)+(4 choose 2)+(4 choose 3)+(3 choose 2)+(3 choose 3) = 10+10+6+4+3+1 = 34 outcomes

iv) I made a table where k = 0,1,2,3 and k=#of white balls drawn

k 0 1 2 3 Fraction 56/220 112/220 48/220 4/220 % 25.4 50.9 21.8 1.8

So I added 21.8% + 1.8% to get 23.6%