Asix-sided number cube is labeled with the numbers 1–6, one number on each face. each number is used exactly once. how many possible outcomes exist when the cube is rolled two times?

36

Step-by-step explanation:

When the cube is rolled two times

Let (a,b) denote a possible outcome of rolling the cube twice , with a the number on the top of the first roll and b the number on the top of the second roll

(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 (a,b).

It can be obtained from the multiplication principle: there are 6 possibilities for a, and for each outcome for a, there are 6 possibilities for b.

So, the total number of outcomes (a,b) is

Hence the total number of possible outcomes is 36