CMSC 203 Fall 2003 Examination 3
1. (a) How many license plates can a state produce if the plates can contain 7 characters (from 26
letters and 10 digits) if they can only use one digit?
(b) How many ways can Mr. Paul choose 8 students from a class of 12 Boys and 17 Girls, if he
must choose at least 6 boys?
(c) How many orderings are there of the letters of the word COMPUTERSCIENTIST ?
(d) How many ways can I select either a RED card or a FACE card (not including ACE) from a
standard bridge deck of cards?
(e) How many ways can I fill a box of 80 chocolates from 30 types if I must have at least 2 of each
type in the box?
2. Let R be the relation on Z given by R = {(a,b) | a,b ∈ Z and a ≡ b mod 10}.
(a) Prove the R is Reflexive. (b) Prove the R is Symmetric.
(c) Prove the R is Transitive. (d) Describe the partition of Z induced by R.
Let S be the relation on {1,2,3,4} given as
S = {(1,2), (1,3), (2,2), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,3), (4,4)}
(e) Graph S.
(f) Find MS, the Matrix of S.
(g) Find MS o MS
(h) Find the Primary Keys and P3,6 for the database:
Make Model Year Engine ID Vehicle ID Color
Ford Mustang 1972 A1222 FO13579 Black
Ford Fiesta 1989 C54322 FO24245 Yellow
Chevy Camaro 1991 754342AH CH172389 Black
Chevy Caprice 1989 442355CC CH156738 Yellow
Olds Cutlass 1992 ANDU33 OL64332 Blue
Olds Cutlass 1992 ANGH28 OL61998 White
Volvo P1800 1969 44325XX VO44526 White
Volvo 240 1986 53526PD VO64690 Black
Volvo 760 1992 578868R VO83529 Blue
3. (a) For a collection of 100 coins, if 45 are quarters, 15 are quarters from the 1990s, and 55 are
coins from the 1990s, what is the probability the a coin chosen at random is a quarter or is a coin
from the 1990s?
(b) What is the probability that a family with 4 children have 3 boys given they have at least 1
boy?
4. (a) Find the truth table for the Boolean Polynomial F(x,y,z) = x’z + xy’
(b) Find the Disjunctive Normal Form (i.e. Sum of Products Form) of the polynomial in part (a).
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