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Q14-5 points 14,890 people attended the first game of the 1984 NBA Finals between the Los Angeles Lakers and the Boston Celtics. Is it a mathematical certainty that at least two of those people shared the same three-letter set of initials (such as JFK or LBJ)? Justify your reasoning.

Q5-6 points What subset ​ ​ of the real numbers would you use to make the function

Q10-6 points Seven people attended a smaller dinner party. Is it mathematically possible that each person shook hands with exactly three people at the dinner? Explain why or why not.            

Q16-5 points Use the Binomial Theorem to write out the expansion of (2a + b)3 .

Q4-5 points Given the following sets: U = ​{1, 2, 3, 4, 5, 6, 7, 8} A = ​{4, 6, 7} B = ​{1, 2, 4, 7} C = ​{1, 3, 5, 6, 8} Find A x A.    

Q9-5 points Use the roster method to describe the set  { 2n + 1 | n ∈ ℤ }.

Q6-5 points Let D  = ​{1, 4, 6, 7, 8}. How many subsets does D have?  

Q19-5 points Consider the sequence: 1, 7, 13, 19, 25, … Find both the 50th term of the sequence and the sum of the first 50 terms.

Q12-5 points Jamar’s Donut Shop sells 6 flavors of doughnuts each day. If repeat flavors are allowed, how many different ways can a three-doughnut box be filled?

 Q13-5 points Jim has a drawer with 6 red socks, 6 blue socks, and 8 black socks. If he picks them out without looking, how many socks must Jim pull out of the drawer to guarantee that he has a matching color pair?