>>11274350Case 1: two yellows drawn
Probability of pulling a yellow on the first draw = 4/12
Probability of pulling a yellow on the second draw = 3/11
Probability of pulling a yellow on the third draw = 2/10
total = 4*3*2/(12*11*10)
Case 2: one yellow drawn
Probability of pulling a yellow on the first draw = 4/12
Probability of pulling a non-yellow on the second draw = 8/11
Probability of pulling a yellow on the third draw = 3/10
total = 4*8*3/(12*11*10)
Probability of pulling a non-yellow on the first draw = 8/12
Probability of pulling a yellow on the second draw = 4/11
Probability of pulling a yellow on the third draw = 3/10
total = 8*4*3/(12*11*10)
Case 3: no yellows drawn
Probability of pulling a non-yellow on the first draw = 8/12
Probability of pulling a non-yellow on the second draw = 7/11
Probability of pulling a yellow on the third draw = 4/10
total = 8*7*4/(12*11*10)
Final = sum(x=0 --> x=2) (9!/12!)*(2!/(x!(2-x)!))(4!/(1+x)!)*(8!/(8-x)!) = 440/1320 = 1/3
