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(3) [12 marks] Suppose that you roll five 6-sided standard, independent dice. (1) If the order of the dice matters e.g. roll (1,2,4,5,6) is different than (4,6,5, 1,2). (2 What is the probability that all five dice show different values? Erample: (1,2,3,4,5) is a roll of this type, but (1,1, 2,3,4) is not. [1 mark| What is the probability that two dice show the same value and the remaining three dice all show different values? Example: (6,1,6,2,3) is a roll of this type, but (1,1,2,2,3) and (4,4,4,5,6) are not. [2 marks] What is the probability that two dice show one value, two different dice show a second value, and the remaining die shows a third value? Example: (6,1, 2,1,2) is a roll of this type, but (4, 4, 4, 4,5) and (5,5, 5, 6,6) are not. [3 marks] ) If the order of the dice does not matter e.g. roll (1,2,4,5,6) is the same as (4,6,5,1, 2). What is the probability that all five dice show different values? Example: (1,2,3,4,5) is a roll of this type, but (1,1, 2, 3,4) is not. [1 mark| What is the probability that two dice show the same value and the remaining three dice all show different values? Example: (6,1,6,2,3) is a roll of this type, but (1,1,2,2,3) and (4,4,4,5,6) are not. [2 marks] What is the probability that two dice show one value, two different dice show a second value, and the remaining die shows a third value? Example: (6,1,2,1,2) is a roll of this type, but (4,4, 4, 4,5) and (5,5,5,6,6) are not. [3 marks]