The sample space for a pair of distinguishable dice is

(1,1)
(1,2)
(1,3)
(1,4)
(1,5)(1,6)
(2,1)
(2,2)
(2,3)
(2,4)
(2,5)(2,6)
(3,1)
(3,2)
(3,3)
(3,4)
(3,5)(3,6)
(4,1)
(4,2)
(4,3)
(4,4)
(4,5)(4,6)
(5,1)
(5,2)
(5,3)
(5,4)
(5,5)(5,6)
(6,1)
(6,2)
(6,3)
(6,4)
(6,5)(6,6)

However, the same pair of numbers often occurs more than once. For instance, this set lists (1, 2) and (2, 1) as separate outcomes. But since we cannot distinguish the dice, how do we tell which one is 1 and which one is 2? To avoid the uncertainty, we list each pair of different numbers only once, so that, for instance, the outcome (1, 2) represents the outcome that once die is 1 and the other 2:

(1,1)
(1,2)
(1,3)
(1,4)
(1,5)(1,6)
(2,2)
(2,3)
(2,4)
(2,5)(2,6)
(3,3)
(3,4)
(3,5)(3,6)
(4,4)
(4,5)(4,6)
(5,5)(5,6)
(6,6)

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