Fall 2007 - CMSC 203 - Discrete Structures - Exam 3
1. How many 32-bit binary strings have at least thirty 1’s?
2. How many can I be dealt a Full House (i.e. 3h3c7d7h7s) in 5-card draw poker?
3. How many orderings are there of the letters of the string UNIVERSITYOFMARYLAND ?
4. How many ways can I seat 4 couples around a circular table if each of the couple must sit together?
5. How many ways can I buy an assortment of 75 nails if there are 12 different lengths of nails and I must
have at least 5 of each length?
6. Let R be the relation on Σ = {0,1}, R = {(a,b) | a,b ∈ Σ4 and density(a) = density(b)}. Show that R is an
Equivalence Relation.
7. Describe the partition of Σ4 induced by R.
8. Graph the relation S on {1,2,3,4,5,6,7} given as S = {(a,b) | (a + b) is prime}.
9. How many ordered pairs 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 P2,3,5 for the automobile database:
Make Model Year Mileage Color Transmission
Ford Mustang 2003 49,213 Red Manual
Ford Taurus 1998 127,344 Silver Automatic
Ford Mustang 2004 51,955 Blue Automatic
Dodge Magnum 2005 33,624 Red Automatic
Dodge Caravan 1994 211,577 White Automatic
Toyota Supra 1996 89,390 Black Manual
Toyota Camry 2002 75,295 White Automatic
Primary Keys = _____________________________ P2,3,5 :
11. What is the probability that a Natural Number less than 50 is prime?
12. What is the probability that a Natural Number less than 50 is prime, given its first digit is 3?
13. Determine whether or not a Natural Number less than 50 is prime is independent of its first digit being
a 3?
14. Find the Disjunctive Normal Form for a 3-way switch that lights a bulb and is configured so that
when two consecutive switches match, the bulb is OFF.
15. Find the Disjunctive Normal Form of the polynomial with Truth Table:
x y z F(x,y,z)x y z F(x,y,z)
1 1 1 1 0 1 1 1
1 1 0 0 0 1 0 1
1 0 1 1 0 0 1 0
1 0 0 1 0 0 0 0
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