Question

Let’s say that you are rolling a single, standard die. A single die has six sides. Each side has a set number of dots as seen in this illustration from one dot up to six dots. No side is duplicated.

A single die.

Given three rolls of the die, what is the probability that you roll exactly two sixes?
Using the combination function

Answer 1

`(5)/(72)`

Explanation:

Notice you have to pick 2 dices of 3 dices with the value you want (6)

`(3!)/(2!) =3` ways (any 6 6 , 6 any 6 or 6 6 any)
Also the probability of a 6 is 1/6. And the probability of NO 6 is 5/6

So the total probability is given by

`3 ((1)/(6) )((1)/(6) )((5)/(6) )=(5)/(72)`