Craps Odds of Hitting All Doubles

The only rolls that matter are 1-1, 2-2, 3-3, 4-4, 5-5, 6-6, 1-6, 2-5, 3-4, 4-3, 5-2, and 6-1. Each one is equally likely.

You have to do six things in order, in order to win:
1. Roll one of the six doubles before rolling one of the six sevens; the probability of this is 6/12, or 1/2.
2. Roll one of the five remaining doubles before rolling one of the six sevens; the probability of this is 5/11.
3. Roll one of the four remaining doubles before rolling one of the six sevens; the probability of this is 4/10, or 2/5.
4. Roll one of the three remaining doubles before rolling one of the six sevens; the probability of this is 3/9, or 1/3.
5. Roll one of the two remaining doubles before rolling one of the six sevens; the probability of this is 2/8, or 1/4.
6. Roll the one remaining double before rolling one of the six sevens; the probability of this is 1/7.

The total probability = 1/2 x 5/11 x 2/5 x 1/3 x 1/4 x 1/7 = 1 / 924.