You roll the same die three times. Consider the possible outcomes if the order of the resultsis not recorded (meaning, e. g., that 1-2-1 and 2-1-1 are considered the same outcome). (a) Order the possible results in lexicographical order and show by direct counting that thenumber of possible outcomes is

Answer: 56 outcomes

Step-by-step explanation:

Tossing a die 3 times and not having the order recorded, we have the following outcome.

[1,1,1] [1,1,2] [1,1,3] [1,1,4] [1,1,5] [1,1,6]

[1,2,2] [1,2,3] [1,2,4] [1,2,5] [1,2,6],

[1,3,3] [1,3,4] [1,3,5] [1,3,6]

[1,4,4] [1,4,5] [1,4,6]

[1,5,5] [1,5,6]

[1,6,6]

[2,2,2] [2,2,3] [2,2,4] [2,2,5] [2,2,6],

[2,3,3] [2,3,4] [2,3,5] [2,3,6]

[2,4,4] [2,4,5] [2,4,6]

[2,5,5] [2,5,6]

[2,6,6]

[3,3,3] [3,3,4] [3,3,5] [3,3,6]

[3,4,4] [3,4,5] [3,4,6]

[3,5,5] [3,5,6]

[3,6,6]

[4,4,4] [4,4,5] [4,4,6]

[4,5,5] [4,5,6]

[4,6,6]

[5,5,5] [5,5,6]

[5,6,6]

[6,6,6]

Hence, By direct counting, the number of possible outcome is 56 outcomes.