# Yahtzee 4 of a Kind

Calculate the probability of 4 of a kind in Yahtzee:

Probability of 4 of a kind = Probability[4(1s or 2s or 3s or 4s or 5s or 6s & unequal 5th die)]

Probability of 4 1's = All possibilities of 4 1's & unequal 5th die * 6 die faces
P(1,1,1,1,not 1) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6
 P(1,1,1,1,not 1) = 5 7,776

Probability of 4 2's = All possibilities of 4 2's & unequal 5th die * 6 die faces
P(2,2,2,2,not 2) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6
 P(2,2,2,2,not 2) = 5 7,776

Probability of 4 3's = All possibilities of 4 3's & unequal 5th die * 6 die faces
P(3,3,3,3,not 3) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6
 P(3,3,3,3,not 3) = 5 7,776

Probability of 4 4's = All possibilities of 4 4's & unequal 5th die * 6 die faces
P(4,4,4,4,not 4) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6
 P(4,4,4,4,not 4) = 5 7,776

Probability of 4 5's = All possibilities of 4 5's & unequal 5th die * 6 die faces
P(5,5,5,5,not 5) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6
 P(5,5,5,5,not 5) = 5 7,776

Probability of 4 6's = All possibilities of 4 6's & unequal 5th die * 6 die faces
P(6,6,6,6,not 6) = 1/6 * 1/6 * 1/6 * 1/6 * 5/6
 P(6,6,6,6,not 6) = 5 7,776

Probability of 4 of a kind = All possible of 4 of a kinds & unequal 5th die * 6 die faces
 Probability of 4 of a kind = (5 + 5 + 5 + 5 + 5) x 6 die faces 7,776

 Probability of 4 of a kinds = 25 x 6 die faces 7,776

 Probability of 4 of a Kind = 150 7776

Using our GCF calculator, we reduce top and bottom by 6, to get
 Probability of 4 of a Kind = 25 1,296