Algebra 2 STUDY GUIDE AII.10, II.12 Permutations/Combinations, Variation
Mrs. Grieser
Name: _______________________________________ Date: ________________ Block: __________
Permutations/Combinations, Variation Equations TEST STUDY GUIDE
Test covers:

Permutations: find number of combinations when order matters, that is, ABC and
BAC are considered different combinations.

Combinations: find number of combinations when order doesn’t matter.

Variation equations: know how to solve problems and find constants of variation for
direct, inverse, joint, and combination variations.
Practice Questions:
1) Evaluate the following without using the calculator except for simple computations:
a) 7!
b)
8P3
c) 3P3
d)
15C5
e)
9
f)  
 2
10C0
2) A library card id follows the following configuration: 3 letters followed by 5 numbers.
How many library cards can be created if
a) letters and numbers can be repeated
b) letters and numbers cannot be repeated
c) letters may not be repeated, but numbers can
3) Find the number of distinguishable permutations in the following words:
a) TROUBLE
4)
b) DOORBELL
c) SURPASSES
d) PANAMA
e) TALLAHASSEE
How many different ways can 8 books be lined up on a shelf?
5) At a blood drive, blood can be labeled one of four types (A, B, AB, or O), one of two Rh
factors (+ or -), and one of two genders (M or F). How many different ways can blood be
labeled?
6) A baseball manager is determining the batting order for the team. The team has 9
members, but the manager definitely wants the pitcher to bat last. How many batting
orders are possible?
7) Find the number of possible 5 card hands in a standard 52 card deck with 4 13-card
suits with 3 picture cards in each suit (jack, queen, king) in each suit:
a) 5 red cards
b) 4 spades and 1 card that is not a spade
c) 2 face cards and 3 other cards that aren’t face cards
d) at least 1 king
8)
A youth indoor soccer team has 6 starting players. The starting players must consist of
3 boys and 3 girls. There are 7 boys and 6 girls on the team. Each player can play each
position. In how many ways can the coach select players to start the game?
Algebra 2 STUDY GUIDE AII.10, II.12 Permutations/Combinations, Variation
Mrs. Grieser Page 2
9) There are 5 people waiting on an elevator to get to the bottom floor, and they are all
equally likely to exit first. How many different ways can they exit the elevator?
10) You are visiting a zoo, and have 7 exhibits left to see. You have time to see 3 more. How
many different combinations of exhibits can you see?
11) The Student Senate consists of 6 seniors, 5 juniors, 4 sophomores, and 3 freshmen.
a) How many different committees of exactly 2 seniors and 2 juniors can be chosen?
b) How many different committees of at most 4 students can be chosen if the minimum
number of students on a committee is 1?
12) Parents have 10 books that they can read to their children this week. Four of the books
are nonfiction and 6 are fiction.
a) If the order in which they read the books is not important, how many different sets
of 4 books can they choose?
b) In how many groups of 4 books are all the books either nonfiction or fiction?
c) Suppose 3 biographies are added which are counted as a separate category from the
other nonfiction book. Suppose the parents want to read 1 non-fiction, 2 fiction,
and 1 biography to their children. How many possible combinations are there to do
this?
13) An orchestra teacher has 10 flute players, and wants to arrange the first three chairs
for them such that one is considered first chair, second chair, and third chair. In how
many different orders can the orchestra teacher arrange the three out of ten flutists?
14) A toy store wants to arrange toys in its front window. The manager wants 8 dolls, 3 toy
cars, and 7 board games in the window. If the store has 18 dolls, 7 toy cars, and 12
board games in stock, how many different arrangements can be made?
15) y varies directly as x2 and inversely as z. If y = 12 when x = 2 and z = 7, find y when x =
3 and z =9.
16) y varies jointly as x and
z . If y = 6 when x = 3 and z = 9, find y when x = 4 and z = 36.
17) Answer the variation questions:
a) Write an equation that represents the statement “t varies jointly with m and n but
inversely with the square v”
b) Find the constant of variation if t=16, v = 3, m = 12, n = 3, and re-write the equation
using the constant of variation.
c) What is the value of t if v = 8, m = 4, n = 12?
18) Strawberries varied jointly as plums and tomatoes. If 500 strawberries went with 4
plums and 25 tomatoes, how many plums would go with 40 strawberries and 2
tomatoes? Find the constant of variation, the equation, and the solution.
19) Reds varied directly as yellows and inversely as greens squared. If 100 reds and 40
yellows went with 10 greens, how may reds went with 20 yellows and only 5 greens?
Find the constant of variation, the equation, and the solution.
Algebra 2 STUDY GUIDE AII.10, II.12 Permutations/Combinations, Variation
Mrs. Grieser Page 3
20) The number of students varied jointly as the number of teachers and the number of
administrators squared. 1000 students were present when there were 5 teachers and 2
administrators. How many students were there with 8 teachers and 1 administrator?
21) The volume of a can varies jointly as the height of the can and the square of its radius. A
can with an 8 inch height and 4 inch radius has a volume of 402.12 in3. What is the
volume of a can that has a 2 inch radius and a 10 inch height? Round your answer to
the nearest hundredth if necessary.
22) The time required to process a shipment of goods at Wal-Mart varies directly with the
number of items in the shipment and inversely with the number of workers assigned. If
15,000 items can be processed by 8 workers in 10 hours, then how long would it take
12 workers to process 20,000 items? Round your answer to the nearest integer.
Review questions:
23) Find the solution(s) to the system, if any:
y = x2 + 6x + 1
y = -2x - 14
24) Simplify: i10 – i24 + i64 – i13
3
4
5
2
25) Simplify: 16  25 125
7
3
26) At a school, 500 student GPAs are normally distributed with a mean of 2.7 and a
standard deviation of .5. How many of these students have a GPA between 3.0 and 4.0?
27) If f(x) = 3x – 4, find f-1(x), its inverse.
28) Which functions are 1-1?
a) f(x) = x3 + 3x - 1
b) g(x)=-2x2 + 7
c) h(x) = bx
d) k(x) = 3x4 - 2
29) Put f(x) = 3x2 + 6x – 18 in vertex form; then find the vertex and the zeros of the function
(use the vertex form to find the zeros).
30) Find the reciprocal of 3i – 2.
31) Simplify:
 64x 
3
6
2
32) Graph the function, stating domain and range in interval
notation:
g(x) =  2 x  1  5 D=_______________ R = ___________
33) Solve: -2|2x + 4| - 5 < -10
34) Factor: 10xy + 14x + 15y + 21
Algebra 2 STUDY GUIDE AII.10, II.12 Permutations/Combinations, Variation
STUDY GUIDE ANSWERS
1) a) 5040 b) 336 c) 6 d) 3003 e) 1 f) 36
2) a) 1,757,600,000 b) 471,744,000 c) 1,560,000,000
3) a) 5040 b) 10,080 c) 15,120 d) 120 e) 831,600
4) 40,320
5) 16
6) 40,320
7) a) 65,780 b) 27,885 c) 652,080 d) 886,656
8) 700
9) 120
10) 35
11) a) 150 b) 4047
12) a) 210 b) 16 c) 180
13) 720
14) 1,212,971,760
15) 21
16) 16
kmn
4mn
b) k = 4; t 
c) t = 3
2
v
v2
17) a) t 
18) k=5; s=4pt; 4 plums
19) k=250; r 
250y
; 200 reds
g2
20) k = 50; s = 50ta2; 400 students
21) k = 3.14 (pi) ; V = 3.14hr2; 125.66 in
22) k = 0.00533; t 
.00533n
; about 9 hours
w
23) (-5, -4) and (-3, -8)
24) -1 – i
25) 75008
26) about 135 students
27) f-1(x)=
x4
3
28) a) and c)
29) f(x) = 3(x+1)2-21; vertex: (-1, -21) ; zeros: -1± 7
30) 
3i  1
13
31) 16x4
32) D=[-1, ∞) R=(-∞, 5]
33) x < 
13
3
and x > 
4
4
34) (2x+3)(5y+7)
Mrs. Grieser Page 4