I am having a hard time wrapping my head around this and am sure that my answers are wrong.
There are three dice.
A. Chance of getting exactly one six on the three dice.
$$(1/6) * 3 = 1/3$$
B. Chance of getting exactly two sixes.
$$(1/6 * 1/6) * 1.5 = 1/24$$
C. Chance of getting exactly $~3~$ sixes.
$$1/6 * 1/6 * 1/6 = 1/216$$
D. Chance of any combination of A, B and C
$$1/3 + 1/24 + 1/216=
72/216 + 9/216 + 1/216 = 82/216$$
Best Answer
A. There is a total of 6^3=216 combinations if you roll 3 dice. There are 5^2x3=75 combinations that you will get one 6. Thus there is a 75/216=25/72 chance of getting only one 6 when rolling 3 dice.
B. There are 5x3 combinations that you will get 2 6s. Thus there is a 15/216=5/72 chance of getting a 2 6s when rolling 3 dice.
C. There is 1 combination where you will get 3 6s. Thus there is a 1/216 chance you will get 3 6s when rolling 3 dice. (Good job you got this correct)
D. There is a 75+15+1/216=91/216 chance of any of them happening.