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Suppose you roll a six sided die three times and record the outcome as an ordered list of length 3 (for example, if you roll

Suppose you roll a six sided die three times and record the outcome as an ordered list of length 3 (for example, if you roll 4, 4, 5 you would write this as 445). In this question you will want to use the Inclusion-Exclusion Principle of Sets. Inclusion-Exclusion Principle of Sets:

Let A and B be two sets. Let n(X) represent the number of elements in set X. Then the number of elements in the union, A B, (ie., the elements in A or B) is: n(A B) = n(A) + n(B) n(A B)

where A B are those elements that belong to both A and B.

(a) How many possible outcomes are there where there is exactly one 6?

(b) How many possible outcomes are there when there is exactly one 1 or exactly one 2?

(c) How many possible outcomes are there where there is exactly one 1 or one 2 or one 6? HINT: You may wish to draw a Venn diagram to help you.

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