Math 118 – Worksheet #03 - Geometry
1. Art went to the mall to buy a shirt for a friend. His style choices for the shirt are silk and
turtleneck. Both of these choices come in yellow, purple, and orange. Which tree
diagram shows the number of shirt choices that are available to Art?
A)
C)
B)
D)
2. A bag contains 5 red marbles and 4 yellow marbles. You are asked to draw 3 marbles
from the bag without replacement. In how many ways can you draw 2 reds and 1
yellow?
A) 80 B) 20 C) 13 D) 2880 E) 100
3. In how many ways can 1 man and 1 woman, in that order, be selected from 9 men and 8
women?
A) 9 B) 72 C) 8 D) 144 E) 17
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Math 118 – Worksheet #03 - Geometry
4. Management. A department store manager wants to display 9 brands of a product along
one shelf of an aisle. In how many ways can he arrange the brands?
A) 387,420,489 B) 81 C) 362,880 D) 9 E) 18
5. At a high school cafeteria, diners can choose one vegetable from a choice of 3
vegetables, one meat from a choice of 3 meats, one serving of bread from among 4
breads, and a dessert from among 4 desserts. How many meal configurations are
possible?
A) 14 B) 144 C) 4 D) 36 E) 48
6. Suppose you are choosing a wall color from among 4 different paint colors and an
accent color from among 2 different paint colors. How many different wall color and
accent color combinations are possible?
A) 7 B) 8 C) 6 D) 11
7. How many different license plates can be made using 3 letters followed by 4 numbers?
A) 10,000,000 B) 12 C) 3120 D) 175,760,000 E) 118
8. License plates. If a state wants each of its license plates to contain 5 different digits,
how many different license plates can it make if any of the digits 0 through 9 can appear
in any of the 5 positions?
A) 120 B) 30,240 C) 100,000 D) 15,120 E) 3024
9. Suppose you are choosing a 2-digit personal access number using digits from 1 through
2 where no digit can be repeated. How many distinct access numbers are possible?
A) 2 B) 6 C) 1 D) 4
10. A combination lock will open when the right choice of three numbers (from 1 to 35) is
selected. How many different lock combinations are possible?
A) 128,625 B) 1225 C) 35 D) 105 E) 42,875
11. How many different arrangements can be made using all of the letters in the word
MOVIE?
A) 142 B) 10 C) 20 D) 130 E) None of these.
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Math 118 – Worksheet #03 - Geometry
12. There are 14 patients in Dr. Ziglar's waiting room. Dr. Ziglar can see 6 patients before
lunch. In how many different orders can Dr. Ziglar see 6 of the patients before lunch?
A) 3003 B) 121,080,960 C) 84 D) 6 E) 2,162,160
13. How many different 7-bead necklaces can be formed using 7 distinctly colored beads?
A) 720 B) 7 C) 360 D) 5040
14. Management. Five candidates for manager of a department store are ranked according
to the weighted average of several criteria. How many different rankings are possible for
the top four candidates if no two candidates receive the same rank?
A) 625 B) 5 C) 20 D) 120 E) 1
15. If 9!  362,880 , evaluate 8! .
A) 45,360 B) 362,871 C) 40,320
16. 10!

7!
A) 720
B) 90 C) 5040
D) 80
D) 720
E) 5, 040
E) 70
17. Evaluate P 10,5 .
A) 30,240 B) 252 C) 210 D) 5,040
E) 720
18. In how many different ways can three red cards be drawn from a standard deck of
cards? (Note: Order of selection is important.)
A) 3432 B) 132,600 C) 15,600 D) 1716
19. A basketball coach must choose 4 players to play in a particular game. (The team
already has a center.) In how many ways can the remaining 4 positions be filled if the
coach has 10 players who can play any position?
A) 210 B) 40 C) 50 D) 120,960 E) 5040
20. How many six-digit numbers can be formed from the digits 1, 3, 5, 7, 8, and 9 if each
digit can be used at most once in each number?
A) 36 B) 7560 C) 33 D) 46,656 E) 720
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Math 118 – Worksheet #03 - Geometry
21. How many six-digit numbers can be formed from the digits 1, 3, 5, 7, 8, and 9 if the
numbers must be even and digits are not used repeatedly? (Hint: Begin with the digit
where there is a restriction on the choices.)
A) 5 B) 36 C) 46,656 D) 120 E) 15,625
22. In a box, there are 5 ribbons in blue and white colors. How many ways are there to
select at least 1 blue ribbon?
A) 31 B) 30 C) 32 D) 15
23. Out of 8 children, how many ways can a family have exactly 1 boy?
A) 336 B) 512 C) 8 D) 64 E) 80
24. Account numbers for Northern Oil Company consist of five digits. If the first digit
cannot be a 0, how many account numbers are possible?
A) 80,000 B) 800,000 C) 90,000 D) 10,000
25. A circular, rotating, serving tray has 8 different desserts placed around its
circumference. How many different ways can all of the desserts be arranged on the
circular tray?
A) 40,320 B) 56 C) 362,880 D) 5040
26. Evaluate C 12,8 .
A) 1,663,200 B) 495
27. Evaluate C 10,10 .
A) 1 B) 0 C) 80
C) 19,958,400
D) 43
D) 715
E) None of these.
E) None of these.
28. Evaluate C 197,195 .
A) 588 B) 19,306 C) 38,612
D) 1,274,196
E) None of these.
29. Find the number of combinations that can be made from 8 objects taken 2 at a time.
A) 56 B) 16 C) 8 D) 18 E) 28
Ans: E
Learning Objective: Count combinations
Section: 10.3
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Math 118 – Worksheet #03 - Geometry
30. Gambling. A game of cards is played with a hand that consists of 5 cards dealt from a
deck of 26 cards. How many different hands of cards are possible?
A) 65,780 B) 7,893,600 C) 130 D) 11,881,376 E) 120
31. Sam, Leila, Ralph, Julio, Elena, and Laura are in the math club. The club advisor can
send one 4-person team to the next Math Team competition. How many different 4person teams can be formed from these six students?
A) 15 B) 24 C) 360 D) 720
32. The mathematics department is sending 9 of its 11 members to a meeting. How many
different sets of 9 members can be selected?
A) 27 B) 55 C) 99 D) 19,958,400 E) 11
33. In how many ways can 10 people be divided into 2 equal groups?
A) 252 B) 90 C) 45 D) 20 E) 30,240
34. Six cards are drawn, without replacement, from a standard deck of 52 cards. How many
sets of six cards are possible?
A) 20,357,980 B) 20,357,490 C) 20,359,580 D) 20,358,520
35. The playbook for the quarterback of the Cowboys has 69 plays. How many different
ways could the quarterback select 4 plays for the first 4 downs?
A) 864,501 B) 20,748,024 C) 1,348,621,560 D) 11,238,513 E) 276
36. Committees. In how many ways can a committee consisting of 3 men and 4 women be
selected from a group consisting of 16 men and 22 women?
A) 7875 B) 4,096,400 C) 12,620,256 D) 560 E) 178,920
37. Find the number of distinguishable permutations of the group of letters.
A)
B)
C)
D)
E)
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Math 118 – Worksheet #03 - Geometry
38. How many different six-letter arrangements can be made from the letters in the word
CIRCLE?
A) 180 B) 360 C) 720 D) 1440
Ans: B
Learning Objective: Count permutations of nondistinct objects
Section: 10.4
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