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Pr in all cases = (number of combos meeting the criterion) / (total combos)
denominator in all cases = (20+15+12) c 3 = 47c3 = 16215
The numerators are:
1) All different: 20 * 15 * 12 = 3600
2) all chocolate 20c3 = 1140
3) all the same (20c3 + 15c3 + 12c3) = 1140 + 455 + 220
4) all not chocolates 27c3 = 2925
Divide each of those by 16215 to get the probabilities.