Calculating Probabilities of a dice roll

[Routaran]

I'm trying to figure out how to correctly workout the probability of rolling 3 6's if I roll 4 dice at a time. If I roll 3 sixes in a row, I don't bother with the last roll
The order in which I roll them doesn't matter
So here are my potential combinations
Combination 1 => x 6 6 6
Combination 2 => 6 x 6 6
Combination 3 => 6 6 x 6
Combination 4 => 6 6 6

Combination 1/2/3 are the same - I used 5/6 on the first roll because I'm assuming I didn't roll a six
(5/6) (1/6) (1/6) (1/6) = (5/1296) = 0.0039
Combination 4
(1/6) (1/6) (1/6) = (1/216) = 0.0046

I add up the different combinations of rolling the 6s
3(0.0039) + 0.0046 = 0.0163
My odds of rolling 3 sixes on 4 rolls is 0.0163

Did I do this correctly?

 

[jbriggs444]

Yes. That is one correct way to proceed. Arranging things so that x is always in the range 1-5 avoids the pitfall of double-counting certain cases. You have successfully accounted for the 4-sixes case as one of the underlying possibilities for case 4.
Rounding in the calculation means that your last digit is incorrect, but it is only off by one.