# Yahtzee Full House

Calculate the probability of a Full House in Yahtzee:

Probability of a Full House = Probability of 3 of a kind and 1 pair

Probability of a Full House = Total Combos of 3 of a kind and 1 pair/All Possible Rolls
Total Combos of 3 of a kind and 1 pair = Combos of 3 of a kind with 3 (1's) and any 1 pair * 6 die faces
Total Combos of 3 of a kind and 1 pair = 1 pair in roll (4,5)(3,5)(2,5)(1,5)(3,4)(2,4)(1,4)(2,3)(1,3)(1,2)
Total Combos of 3 (1's) and 1 pair * 10 = (1-1-1-2-2) + (1-1-1-3-3) + (1-1-1-4-4) + (1-1-1-5-5) + (1-1-1-6-6) * 10
Total Combos of 3 (1's) and 1 pair * 10 = 5 * 10
Total Combos of 3 (1's) and 1 pair * 10 = 50

Combos of 3 of a kind with 3 (1's) and 1 pair * 6 die faces = 50 * 6
Total Combos of 3 of a kind and 1 pair = 300
Total Possible Die Roll Combos = 6 * 6 * 6 * 6 * 6
Total Possible Die Roll Combos = 7,776

 Probability of a Full House = Total Full House Combos Total Possible Die Roll Combos

 Probability of a Full House = 300 7776

Using our GCF calculator, we reduce top and bottom by 12, to get
 Probability of a Full House = 25 648