CMSC 203 Fall 2005 Examination 3
1. How many 8-bit ASCII words of length 8 are there?
2. How many ways can a teacher choose 8 students from a class of 20 Boys and 15 Girls, if she must
choose no more than 2 girls?
3. How many orderings are there of the letters of the word DISCRETESTRUCTURES ?
4. How many ways can I seat 10 people around a circular table?
5. How many ways can I fill a box of 50 chocolates from 10 types if I must have at least 2 of each type in
the box?
6. Let R be the relation on Σ = {0,1} given by R = {(a,b) | a,b ∈ Σ4 and d(a) = d(b)}. Show that R is an
Equivalence Relation.
7. Describe the partition of Σ4 induced by R.
8. Graph S, the relation on {0,1,2,3,4,5,6} given as S = {(a,b) | a + b < 4}.
9. How many elements are there in the Equivalence Relation, R, that induces the partition:
{{1,2,3,4}, {5,6}, {7,8,9}, {0}} of {0,1,2,3,4,5,6,7,8,9)?
10. Find the Primary Keys and P1,6 for the trumpet database whose entries form the following table:
Make Model Year Serial No. Key Finish
Conn 38A 1955 105523 Bb Silver
Conn 40B 1938 52234 Bb Brass
Conn 22A 1966 212203 C Silver
Olds Super 1968 524366 Bb Silver
Olds Super 1952 161230 C Gold
Olds Mendez 1969 210658 Bb Silver
Selmer Radial 1953 14522 Bb Gold
Selmer Paris 1959 18502 Bb Silver
Selmer Radial 1974 64299 C Brass
11. What is the probability that a 4-bit integer is prime?
12. What is the probability that a 4-bit integer is prime, given the first (most-significant) bit is 1?
13. Determine whether or not a 4-bit integer is prime is independent of its first bit being 1?
14. Find the Disjunctive Normal Form for a 3-way switch that lights a bulb and is configured so that
when all 3 switched are ON, the bulb is OFF.
15. Find the Conjunctive Normal Form of the polynomial with Truth Table:
x y z F(x,y,z)
1 1 1 0
1 1 0 1
1 0 1 1
1 0 0 1
0 1 1 0
0 1 0 0
0 0 1 1
0 0 0 1
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