The probability that X = 2 is given by
C(12,2)* C(8,6) / C(20,8) = about 1.47%
The probability that X ≤ 2 = probability that none, one or two of the two slot models are chosen =
C(12,0)* C(8,8) / C(20,8) + C(12,1)* C(8,7) / C(20,8) + C(12,2)* C(8,6) / C(20,8) = about 1.54%
The probabliity that X ≥ 2 = 1 minus the probability that none or one of the two slot models are chosen =
1 - [C(12,0)* C(8,8) / C(20,8) + C(12,1)* C(8,7) / C(20,8)] = about 99%
