Counting

A coin is flipped eight times where each flip comes up with either heads or tails how many possible outcomes? a) contain exactly 3 heads b) contain at least 3 heads c) contain the same number of heads n tails.

Counting

7 women and 7 men are in the department of mathematics. How many ways are there to select a comittee of 5 members if at least 1 woman and least 1 man must be on the committee?

Discrete Math

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Proof -- Equivalence Relations

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Equivalence Relation 2

(See attached file for full problem description) --- Seeking clarification on this problem and how it should have been addressed. Made a wrong assumption somewhere.