a!b!c!...

Key Equations:

Permutations: nPr = (n- r)!

Permutations with Identical Items.

Factorial: n! = n x (n - 1) x (n - 2)x... x3 x2 X 1 n!

n!

• Name:

Date:

MDM 4U UNIT 1 (CHAPTER 4 TEST) • PERMUTATIONS and ORGANIZED COUNTING

K&U APP COM TIPS

22 19 10 14

•

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1. Write as a single factorial. (4 K) a. 3X 2 X 4 X 5 X7 X 6

- 1 I

b. 72 X 7!

= 9 )(SX -1 !

/

c. (n 2-9n+20)(n-6)!

( n - min -5)0-0 1.

(n-k1)‘

2. Evaluate. (3 K) .5 3

15! ismyx13x‘2.?“1)4.€5 3!8!

/.3')< -ZX

ks-AkLi x13X12v-IIK

5 44051-40

b. 7P3(25 -4P2) + 7!/3! + 11(7P3 + 0!)

Z1° ( %.2-) 4 (840) -1.- 11 (2/0-1)

zt o + gip z 3 2... 1

5S9 I

3. Solve for n. (4 K, 2 A)

2(nP5) = n-1P6

2L = (1") (n-5)1 GI- -

2. [r r‘ 141 (n-

(r‘ - 1)

Z (n (.1.116(A-A(t-776(n-At-ep

- )Cyl-Acrybo-A111-061-()64.

2 n 01-s-')(o-6) 2n=n2-IIn ~ 3 (

n 1*- 13n + 3o o = (n 3)

4. Simplify. (2 K) (n — 1)!

(n2 — n)(n — 2)!

a.

o n = Z

n=

If)

5 SCA3

f›rt Se- F.(2- Z ol(-Gierri

foss% b 141es

4.

5r •

rb

SkII

Name:

5. How many different ways can you

arrange all of the following items in a

line? (1K)

4104- t©44x:x0)-->- ©40 4.9 (31.2.

1 81 _ G 2210Zo8oO 4 toz,12,12)

19 2 2-4-1S2

6. A Chinese restaurant features a lunch

special with a choice of wonton soup or

spring roll to start, sweet and sour

chicken balls, pork, or beef for the main

dish, and steamed or fried rice as a side

dish. Create a tree diagram to show all

the possible lunch special at this

restaurant. How many different

possibilities are there? (2K,1A)

8. Kenya has a die and a coin. She rolls the die

and then tosses the coin. Make a tree

diagram to show the possible outcomes.

How many different outcomes are there?

(2K,1A)

VDSSA:11 ‹. 0 0

Date:

9. In how many ways can you roll a sum of 6 or

a sum of 10 with a pair of dice?(1A)

2. 3 4-1 s- (4, -TVN-ert_ a_ce

8.. watts .

I 3 LI s- 2 3 LI s-

3 s fe) 2 (ID 5- 1

8 9 S -7 2,

7

7. Canadian postal codes consist of

alternating 3 letters and 3 numbers (L#L

#L#). How many different postal codes

are possible? (2A)

2- (0 X 1b)t. 2/0•4-10t240 L

1 S- 1 (o (:) ( 0

10. In how many ways can a set of eight books

be arranged on a shelf so that volumes one

and two are beside one another? (2A, 1C, 1T) vt we cor V•0..vc_ k Alen 2. or 2.-Pra.n

X 2 ---- LI ea Y.2.

= 1 06 $3, b •

12. How many permutations of the word

committee begin or end with an e? (2T)

be3olnir43-: 53

z'2 1

4-f - e y ■ !

_ 1008 0

•

• Name:

11. In how many ways could you arrange a

• display of stationary supplies consisting

of 14 notebooks, 5 packages of lined

paper, and 50 pens if all the items are laid

out in a row? (1A)

n = 69

G91 -to

Is-p/ :7 5 .5g ( X tC) ryl

lobgbi ioc 201(00

• -1.-Vvere_ ace_ zo% (13 o etrOlu-i-cklI6115

13. Seven children are to line up for a

photograph.

a. How many different arrangements are

possible?(1K)

!

b. How many arrangements are possible if

Brenda is in the middle?(1A)

z

Date:

14. Bill works in an ice cream store for the

summer months. How many different cones

can Bill create if he has chocolate, mint

chocolate chip, vanilla, maple walnut, and

pistachio ice cream available and a cone can

have at most 3 scoops? (4-r,1c)

--ro+0,A b -C- ctaAJC,u-r- S = 5

3 scoops = 5P3 = (00

Swo9S = 51°2_ = 2_0

scboV .; 5

0 c- ov-kereak- cones = (3o-1- zuts $ S

-1-4(vCre_ 0--re c/.1:-Feete-M- Clyne_s‘

15. How many possible arrangements are there

for the letters in the work BANANA? (1A) 4, I

z)-6, = Go

16. Express as a single term from Pascal's

triangle. (2K) a. ti2,4 + t12,5 = -€.

%3

b. t14,4 t13,4 =

19. A university has a telephone system in

which extension numbers are three digits

long with no repeated digits and no Os.

The university has 492 telephones at

present and is planning to add another 35

in the near future. (3A,3C)

a. Should the university change its system?

Why or why not?

= soq cerk.on

Lfctz.+ Sc= 579- ncesAed ► ■ C‘R--C ,

u_niveirsktt- shay.0.613x.cy e The i+ ̀ S stern bei20-use

, --1-k40-4C0-11

on l9 Ivvate SW`( diffeXents bus

-ev‘ey b. The Drama Department uses extensions

that begin with 3. How many extensions

can the Drama Department have with the

current system?

xsKi -7- 5(0 e_x-i-t ► r -ton (3)

20. A checker is placed on a checkerboard as

shown. The checker may move diagonally

upward on the white squares only. It cannot

move into a square with an X, however, it can

jump over the X into the diagonally opposite

square. How many paths are there to the top

row of the board? (2A)

12i- i2+11 = 4S Fo -t-V■ S.

21. Calvin is trying to get home without running

into Moe the bully (who will steal his lunch

money). However, Calvin does not know what

path Moe is waiting at. Based on the diagram

below, how many possible routes are there so

that Calvin won't lose his lunch money

assuming that he always moves towards his

house? (2A) 3

3 + 31 3 3 -- woes

Date:

•

Name:

17. Casey has 5 trophies. In how many

different arrangements can she put the

trophies on a shelf if she must put on at least three trophies on the shelf? (3T,1C)

3 of rekort- tro(Aies

s P3 = (oo

5Py =17_O

S p y-= 120

61::> fi 12O r 120 = 3 4:) Ll di-QC-emit

wai6s

18. Which row of Pascal's triangle has terms

that sum to 524288? (1K)

)( z-- SV-128g

X t o3 2 = lus 5 2 y egg

= I

• Name: Date:

• 22. Lisa is planning the seating for the head table at a gala. The eight speakers will all be seated along

one side of the table. Richard wants to sit beside Hang, and Lisa knows that Thomas and Lily

should not be seated together, as they have just broken up. In how many ways can Lisa make up

the seating plan? Explain your reasoning. (4C, 4T)

Richard A 1-to..Y\5 act as I kn its 4exe_ are_ now 1 va ►=4-s (now._ caDo-ra

)( 2_ = 5oLko x2. = too80

cAtka R. (chard, Car be Silt

0 ,n _vvvc \ 64 or riNit

use m ci-h 8. Tho rras unit R ccharchl }65,

wc, ►* So A- neck ceCe_ 110W 6 S klz) 1/4_02 °-.(73"- "Z4

6 X 2 X 2- = 288 71/4 IC ec■fetra, fko i_c s 6 11-kon'aS co:ex k>c_ n (el-kJ

col V-Je._ 61, \ eh- 6 r- e ct 4 tor •C‘.' \(1 -1- • T°43*- — 4 s se' 11 \°"1-5 s 4-6AI oAce-e1+-

ll c--k‘rveir. 1008 0 — 2g 8o -; 7 2-0

•