MDM 4U UNIT 1 (CHAPTER 4 TEST) - Ms. Ng's...
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Transcript of MDM 4U UNIT 1 (CHAPTER 4 TEST) - Ms. Ng's...
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
•
•
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
•