How many different outcomes are possible when a pair of dices, one red and one w

Question

How many different outcomes are possible when a pair of dices, one red and one white are rolled two consecutive times? Consider that one roll consists of outcome that is formed by the PAIR of what is on white and red and count the number of outcomes if A) it is possible to distinguish which roll was first and which was second. B) it is not possible to distinguish first and second roll. (Consider that first and second roll are distinguishable as well as the case where they are not. Note that one roll is, which is red and white dices is equivalent to a roll of a dice with 36 sides.)

Explanation / Answer

When rolling two dice, distinguished between them in a red and a white. Let (R,W) denote a possible outcome of rolling the two die,
with R the number on the top of the first die and W the number on the top of the second die.
Note that each of R and W can be any of the number from 1 through 6.
(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)
There are 36 possibilities for (R,W). This total number of possibilities can be obtained from the multiplication principle:
there are 6 possibilities for R, and for each outcome for R, there are 6 possibilities for W. So, the total number of joint outcomes (R,W) is 6 times 6 which is 36.
The set of all possible outcomes for (R,B) is 36.

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