Question

in the game of yahtzee,, on the first roll five dice are tossed simultaneously. what is the probability of rolling five of a kind on the first roll?

Answer 1

The probability of rolling any specific number on a fair die is 1/6.
Therefore the probability of rolling five of a kind is:
$(\frac{1}{6})^{5}=\frac{1}{7776}\ or\ 0.000129$

Answer 2

On rolling five dice, each die will give either of the six numbers from 0 to 6. Thus, the sample space is equal to 6^5 which equal to 7776. If the dice should have unique numbers, the first die can take any of the 6. The second can take only 1 of the 5, and so on. The numbers may appear in 6x5x4x3x2 ways which is equal to 720. Dividing this value by 7776 gives an answer of 5/54.