CMSC 203 Fall 2004 Examination 3
1. (a) How many license plates can a state produce if the plates can contain 6 characters (from 26 letters
and 10 digits) if they can only use one letter?
(b) How many ways can the teacher choose 6 students from a class of 10 boys and 13 girls, if he must
choose at least 5 boys?
(c) How many orderings are there of the letters of the word ELECTRICALENGINEER ?
(d) How many ways can I seat 10 people around a circular table, if a certain pair of people cannot sit next
to one another?
(e) How many ways can I fill a box of 75 chocolates from 20 types if I must have at least 1 of each type in
the box?
2. Let R be the relation on Z given by R = {(a,b) | a,b ∈ Z and a2 + 5 = b2 + 5}.
(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 {1,2,3,4,5} given as
S = {(1,1),(1,4),(1,5),(2,1),(2,3),(3,1),(3,2),(3,3),(3,4),(3,5),(4,3),(4,5),(5,2),(5,4),(5,5)}
(e) Graph S. 2
13
45
(f) Find MS, the Matrix of S. (g) Find MS o MS
(h) Find the Primary Keys and P3,6 for the database whose entries form the following table:
Make Model Year Engine ID Vehicle ID Color
Ford Mustang 1972 A1222 FO13579 Black
Ford Fiesta 1989 C54322 FO24245 Yellow
Chevy Camaro 1972 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 50 coins, if 22 are quarters, 15 are quarters from the 1990’s, and 35 are coins
from the 1990’s, what is the probability the a coin chosen at random is a quarter or is a coin from the
1990’s?
(b) What is the probability that a couple planing to have 4 children will have 2 boys given their first child
is a boy?
(c) Show that having 2 of 4 children be boys is INDEPENDENT of their first child being a boy.
4. (a) Find the truth table for the Boolean Polynomial F(w,x,y,z) = w’x’z + x’y
(b) Find the Disjunctive Normal Form of the polynomial in part (a).
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