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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?

Q19-5 points Consider the sequence: 3, 8, 13, 18, 23, … Find both the 50th term of the sequence and the sum of the first 50 terms.

Q10-5 points Viola has a bookshelf with seven books on it. In how many ways can they be arranged?  

Q5-5 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 C ∩ B.

Q10-5 points Michael has five different sport coats hanging on a closet rod. In how many ways can they be arranged? 

Q14-6 points Prove the statement (if true), or disprove it by giving a counterexample (if false)                If n is an integer and n²​ is divisible by 4, then n is divisible by 4.

Q17-5 points Solve by backtracking for an explicit formula for the recursive sequence: a1​ = 4 an​ = -3a​n-1

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} Let D = B – A. Find D x D.

Q18-5 points Solve the recurrence relation: b1​ = 3 b2​ = 5 bn​ = 2​bn-1​ −​ b​n-2