Ch 2 Review
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New York University *
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Course
131
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
5
Uploaded by ProfessorWren643
3. Given the sets A ={Maria, Nobuko, Leroy, Mickey, Kelly} and B = {Rachel, Leroy, Deanna, Mickey}, find the following.
a. A U B
b. A ∩
B
5. Given n(U)=61, n(A)=32, n(B)= 26, and n(AUB)= 40, do the following
a. Find n(A B).
b. Draw a Venn diagram illustrating the composition of U.
10. A survey of 1,000 college seniors yielded the following information: 396 seniors favored capital punishment, 531 favored stricter gun control, and 237 favored both.
a. How many favored capital punishment or stricter gun control?
Kelly
Tang
chZReviewP.BZ
-134
#
3,510-1413,17-19,2423-28,43
{
Maria
,
Nobuko
,
Leroy
,
Mickey
,
Kelly
,
Rachel
,
Deanna
}
{
Leroy
,
Mickey
}
n
32-126=58
58-40=18
A
B
40-32=8
8
18
14
40-26=14
21
61-40=21
capital
stricter
396-237=159
2371-294-1159=690
159
237294
531-237=294
1000-690=310
310
396-1531-237
927-237
=
690
b. How many favored capital punishment but not stricter gun control?
c. How many favored stricter gun control but not capital punishment?
d. How many favored neither capital punishment nor stricter gun control?
11. A survey of recent college graduates yielded the follow- ing information: 70 graduates earned a degree in mathematics , 115 earned a degree in education, 23 earned degrees in both mathematics and education, and 358 earned a degree in neither mathematics nor education.
a. What percent of the college graduates earned a degree in mathematics or education?
b. What percent of the college graduates earned a degree in mathematics only?
c. What percent of the college graduates earned a degree in education only?
159
294
310
math
education
70-23--47
115-23=92
472392
358
47123-192-1358=520
47-123-192--162
162
520=0
154=31.154%0
47
520--0.0%038=9.038
%
92
520--0
69247.692%
13. An exit poll yielded the following information concerning people’s voting patterns on Propositions A, B, and C: 305 people voted yes on A, 95 voted yes only on A, 393 voted yes on B, 192 voted yes only on B, 510 voted yes on A or B, 163 voted yes on C, 87 voted yes on all three, and 249 voted no on all three. What percent of the voters voted yes on more than one proposition?
17. Sid and Nancy are planning their anniversary celebration, which will include viewing an art exhibit, having dinner, and going dancing. They will go either to the Museum of Modern Art or to the New Photo Gallery; dine either at Stars, at Johnny’s, or at the Chelsea; and go dancing either at Le Club or at Lizards
a. In how many different ways can Sid and Nancy celebrate their anniversary?
b. Construct a tree diagram to list all possible ways in which Sid and Nancy can celebrate their anniversary.
305-1393--698
698-510=188
188-87=101
A
B
305
-
(101-1951-87)=305-283--22
393-(19241011-87)=393-380--13
95
101
192
163-122+87+137=163-122--41
87
22
13
951-101-1224871-13
-11921-411-249=800
41
a
zyg
101-1871-22+13=223
Zg%q=qzy875=
27.875%
2.
3.2=12
MMA
/
stars
/
"
"
"
b
-
Leclub
Wizards
/
starsllizards
-
Johnny
's
-
leclub
NPG
-
Johnny
's
-
Leclub
Wizards
Wizards
Chelsea
_teaub
Chelsea
_teaub
Lizard
Lizard
{
MMA-S-LGMMA-S-L.MN/A-J-L4MMA-J-4MMA-C-Lc,NPG-S-LCiNPa
-5-4
NPG-J-LC-NPG-J-4NPG-c-LC.MG
-
GL
}
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18. A certain model of pickup truck is available in five exterior colors, three interior colors, and three interior styles. In addition, the transmission can be either manual or automatic, and the truck can have either two-wheel or four-wheel drive. How many diferent versions of the pickup truck can be ordered?
19. Each student at State University has a student ID number consisting of five digits (the first digit is non- zero, and digits can be repeated) followed by two of the letters A, B, C, and D (letters cannot be repeated). How many different student numbers are possible?
21. In how many ways can you select three out of eleven items under the following conditions?
a. Order of selection is not important.
b. Order of selection is important.
23. A group of ten women and twelve men must select a three-person committee. How many committees are possible if it must consist of the following?
a. one woman and two men
b. any mixture of men and women
c. a majority of men
5.
3
•
3
•
I
•
I
•
2
.
-4=360
9
•
10
.
10
.
10
.
10
•
4
•
3
=
1,080,000
11C
}
=
165
II.
10.9=990
10C
,
•
126--10.66=660
10+12=22
224--1540
Case
/
it
woman
Zhen
104
•
1212=10
•
66--660
660-1220=880
case
2
:3
men
+12C
}
+220
24. A volleyball league has ten teams. If every team must play every other team once in the first round of league play, how many games must be scheduled?
25. A volleyball league has ten teams. How many different end-of-the-season rankings of first, second, and third place are possible (disregarding ties)?
26. Using a standard deck of fifty-two cards (no jokers), how many seven-card poker hands are possible?
27. Using a standard deck of fifty-two cards and two jokers, how many seven-card poker hands are possible?
28. A 6/42 lottery requires choosing six of the numbers 1 through 42. How many different lottery tickets can you choose?
43. What is the difference between permutations and combinations?
106=45
•
9-
•
1=720
52C
7--133,784,560
521-2=54
544--177,100,560
426--5,245,786
For
permutations
,
the
order
matters
and
order
doesn't
matter
for
combinations
.