CMSC 250 – Jerry Alan Fails Student: __________________
Due: Tuesday, July 10, 2007 ID #: __________________
HW #10 Due: Tuesday, July 10, 2007 Page 1 of 2
HW #10
You must work alone on your homework, and homework must be written legibly, single-sided
on your own lined paper, or typed, with the answers clearly labeled and in the sequential order
as assigned. You must write your name and university ID number in the upper right-hand corner
of your homework. Staple all pages together and be sure that your name appears on every sheet.
1. (4 points) Write your name clearly on each page. Write the time and place of Exam 2.
2. (15 points) Let P(A) be the power set of A. Prove that for all sets A and B,
)()()( BPAPBAP
∩
=
∩
.
3.
(10 points) Consider the following statements:
100 students are majoring in CS, Math, and/or Engineering
20 CS students are also engineering majors, but are not Math majors
10 CS students are also math majors students
40 students are CS majors only
15 students are majoring in both Math and Engineering
25 students are math majors
5 students are majoring in all three
(a)
(2 points) How many CS majors are there?
(b)
(2 points) How many Engineering students are there?
(c)
(2 points) How many students are only majoring in Engineering?
(d)
(4 points) Draw and label a Venn diagram indicating how many students are in each
subset.
4.
(10 points) Consider the numbers 1 through 99,999 in their ordinary decimal representations.
How many contain exactly one of each of the digits 2, 3, 4, and 5?
5.
(15 points) Answer the following:
(a)
How many integers from 1 through 100,000 contain the digit 6 exactly once?
(b)
How many integers from 1 through 100,000 contain the digit 6 at least once?
(c)
If an integer is chosen at random from 1 through 100,000, what is the probability that it
contains two or more occurrences of the digit 6?
6.
(12 points) Answer each of the following:
(a)
How many distinguishable ways can the letters of the word MILLIMICRON be arranged
in order?
(b)
How many distinguishable orderings of the letters of MILLIMICRON begin with M and
end with N.
(c)
How many distinguishable orderings of the letters of MILLIMICRON contain the letters
CR next to each other in order and also the letters ON next to each other in order?
