Is the odds of 1,2,3 and 6,6,6 the same in a 3-dices game ?

Question

if i roll 3 dices with six sides, will the odds of getting 1,2,3 the same as 6,6,6.

Answer 1

yes, odds are any combination of three numbers are equally likely.

Answer 2

no the chances for all dice to be showing sixes is lower then getting 1,2,3.

To elaborate:

for 666 you need each and every dice to roll a 6. That's 1 out of 216 possible combinations.

for 123 your first die could be a 1 then the second be a 2 or 3 and the third takes what's left, so 2/216 here. same for rolling a 2 or a 3 with the first, so you end up with 6/216 or 1/36.

Answer 3

yup its all the same.

Answer 4

If order doesn't matter (i.e., 3-1-2 is the same as 1-2-3), then no.  Consider the odds:

Odds of a getting a 6 on any die = 1/6

Odds of getting 6-6-6 = 1/6 * 1/6 * 1/6 = 1/216

Odds of getting a 1, 2, or 3 on the first die = 1/2

Odds of getting one of the other two numbers on the 2nd die = 1/3

Odds of getting the remaining number on the last die = 1/6

Odds of getting a 1, 2, and a 3 = 1/2 * 1/3 * 1/6 = 1/36

If order matters (that is, you have to roll a 1, then a 2, then a 3), the the odds would be the same - i.e., 1/216.