Homework Chapter 2.6 Combinatorics
A
NAME:_________________
2.6.2 A coded message from a CIA operative to her Russian KGB counterpart is to be sent in the form Q4ET, where the
first and last entries must be consonants; the second an integer 1 through 9; and the third,, one of the six vowels. How
many different ciphers can be transmitted?
43
am
A 21
integare
B 9
C 6vowell
C
21 9 6 21 123,8142
2.6.3 How many terms will be included in the expansion of: (𝑎 + 𝑏 + 𝑐)(𝑑 + 𝑒 + 𝑓)(𝑥 + 𝑦 + 𝑢 + 𝑣 + 𝑤)
Which of the following will be included in that number: aeu, cdx, bef, xvw ?
3 3 5 45
I
andaev.cl
2.6.12 In international Morse code, each letter in the alphabet is symbolized by a series of dots and dashes: for example,
the letter A is encoded as “dot dash.” What is the minimum number of dots and/or dashes needed to represent any letter in
the English alphabet? (note, that Morse code will use any number of dots and dashes to encode the alphabet (i.e, the letters
may not use the same number of symbols, since we won’t need blank or filler symbols).
2A6TeEE
2
variable
2.6.17 The board of a large corporation has six members willing to be nominated for office. How many different
“president/vice president/treasurer” combinations could be submitted to the stockholders?
7T
65 4
1200
2.4.22 Four women and four men are to be seated in a row of chairs numbered 1 through 8.
a. How many total arrangements are possible?
b. How many arrangements are possible if the women are required to sit in alternate chairs?
9
8
40132L
1,152
in
hi
2.4.34 Which state name can generate more permutations, TENNESSEE or FLORIDA ?
29
21
4510
TENNLSSEE
E.IT
7 5140
2.4.35 How many numbers greater than 4 million can be formed from the digits: 2, 3, 4, 4, 5, 5, 5 ?
total
of ways
420
t
offmy
3
13609
60
3R
8 books, three with red covers, three with blue
2.4.36 An interior decorator is trying to arrange a shelf containing eight
covers, and two with brown covers.
2Br
a. Assuming the titles and the sizes of
the books are irrelevant, in how many ways can he arrange the eight books?
b. In how many ways could the books be arranged if they were all considered distinct?
c. In how many ways could the books be arranged if the red books were considered indistinguishable, but the other five
books were considered distinct?
2
c
83
1560J
b 81 140,322
8 716 5 4 16,7202
3131
2.6.42 In how many ways can the word ABRACADABRA be formed in the array pictured here?
Assume that the word must begin at the top A and progress diagonally downward to the bottom
A. (example shown in red)
NA
2.6.50 How many straight lines can be drawn between any two points, given these five points total (A, B, C, D, E)?
522
25
5
5.21
3
D
2.6.52 A boat has a crew of eight, with places for four people on each side. Two of those eight can row only on the stroke
side, and three of these eight can row only on the bow side. In how many ways can the two sides of the boat be crewed?
crew 8
5 8 row
bow
3
41 4
24024
3C
3
11,7282
2.6.53 Nine students, four women and five men, interview for four summer internships sponsored by a city newspaper.
a. In how many ways can the newspaper choose a set of four interns?
b. In how many ways can the newspaper choose a set of four interns if it must include two women and two men?
c. How many sets of four can be picked such that not everyone in a set is of the same gender?
a
964
4
5,511263
01 4
5