What are the odds of rolling 1 2 3 4 5 6 with six dice?

Answer 1

You have a one out of six chance of rolling a 1 to start off with

1/6

You then have a one out six chance of rolling 2 next, so you have a 1/6 x 1/6 chance of rolling 1 followed by 2

1/6 x 1/6 = 1/36

You then have a one out six chance of rolling 3 next, so you have a 1/6 x 1/6 x 1/6 chance of rolling 1 followed by 2 followed by 3

1/6 x 1/6 x 1/6 = 1/216

etc

You have a (1/6)6 chance of rolling 1 2 3 4 5 6 = 1/46656

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While the above is true if you intend to roll specifically a 1-2-3-4-5-6, the logic above does not allow for rolling a 1-3-2-4-5-6 which, with dice, would also be considered a 1-2-3-4-5-6. The same goes for a 1-4-6-2-3-5, etc.

The odds of rolling ANY 1-2-3-4-5-6 combination with 6 dice is roughly 65:1.

6/6 * 5/6 * 4/6 * 3/6 * 2/6 * 1/6 = 720/46656 = 64.8:1

Explanation:

The first die can be any number, then you subtract 1 from the numbers remaining on down to the last die.