CSE321 Midterm No. 2 December 1, 1995

All questions count equally. Answer each question in the space provided.

1. Compute the greatest common divisor of 56 and 21 using the euclidean algorithm. Show all intermediate results.
2. Give a simple formula for .
3. Twelve houses are located in a row along a city block. Four of the houses are new and the other eight are old. Asssuming that all orderings of the twelve houses along the row are equally likely, what is the probability that the four new houses are consecutive?
4. Solve the recurrence .
5. Let E and F be events in a sample space. Prove:
   

6. Let R be the relation on the set of ordered pairs of positive integers such that if and only if ad = bc. For example, . Prove that R is reflexive, symmetric and transitive.

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