MATH 230

TEST I

Fall 1999

Bellamy & Williford

Each problem counts 20 points.

1. 20 Points

   Let A = {1,2,a,b}; let B = {b,c,2,3}
   
   1. List the elements of
   2. List the elements of
   3. List the elements of
   4. Verify directly by substituting in the numbers that in this case.
   5. Which has more elements, or Justify your answer.

2. 20 Points

   A club has seven members.
   1. How many different committees of three of the members are possible?
   2. How many are possible if two of the members, Bill and Sam, cannot serve on a committee together?

3. 20 Points

   A market researcher has hired a statistical consultant who reports that of the 161 households in a small community, eighteen do not own a computer, forty do not own a microwave, and three do not own a car. Every household owns at least one of these three items and 110 of them own all three. One of the households owns neither a car nor a microwave and one neither a car nor a computer. How many own neither a computer nor a microwave.

4. 20 Points

   To preserve privacy and anonymity, in a certain medical experiment patients are identified by a code consisting of two letters followed by three distinct non-zero digits. The two letters are chosen from the set {B, C, D, E, F, G, H, J, L, M, N, P, Q} and may or may not be the same.

   How many different codes can be constructed by this scheme?

5. 20 Points

   A coin is tossed over and over again until either two heads(H) or three tails(T) have appeared. How many different sequences of outcomes (H or T) are possible?