# Yahtzee 3 of a Kind

Calculate the probability of 3 of a kind in Yahtzee:

Probability of 3 of a kind = 3 of 1 Kind and any unequal 4th & 5th die/All Possible Rolls
Three of a kind combos of (1-6) = Three of a kind combos of 1 * 6 die faces
Three of a kind combos of 1 = (1-1-1-2-3)+(1-1-1-2-4)+(1-1-1-2-5)+(1-1-1-2-6)+(1-1-1-3-4)
(1-1-1-3-5)+(1-1-1-3-6)+(1-1-1-4-5)+(1-1-1-4-6)+(1-1-1-5-6) = 10 possible 3 (1's) & any other 2 non equal die

Total Combos of 2 non-equal die positions = 2 * (4,5)(3,5)(2,5)(1,5)(3,4)(2,4)(1,4)(2,3)(1,3)(1,2)
Total Combos of 2 non-equal die positions = 2 * 10
Total Combos of 2 non-equal die positions = 20

Three of a kind combos of 1 = 10 * 20
Three of a kind combos of 1 = 200
Three of a kind combos of 1 * 6 die faces = 200 * 6
Three of a kind combos of 1 * 6 die faces = 1,200

Total Possible Die Roll Combos = 6 * 6 * 6 * 6 * 6
Total Possible Die Roll Combos = 7,776

 Probability of 3 of a kind = Total Three of a kind Combos Total Possible Die Roll Combos

 Probability of 3 of a kind = 1200 7776

Using our GCF calculator, we reduce top and bottom by 48, to get
 Probability of 3 of a kind = 25 162