When we roll one die, we have a 1 in 6 probability of getting any particular number on the die. When we roll a pair of dice, there are 36 different pairs that can be produced, yet only 11 actual distinct values.

Explain how the probability associated with the roll of each individual die in the pair explains the higher variability in the total outcome of the roll of each pair. How do the concepts of permutations and combinations apply to this example? Discuss how the notion of degree of freedom can be used to illustrate the accumulating results of a set of dice rolls.