KU
/18
MDM 4U0 Permutations Assignment (c)
Name:
APP /15
COM Level: 0 1 2 3 4
/5
1) While shopping for a new suit, Ed finds three pairs of pants he likes as well as three pairs
of shoes & five different jackets. In how many ways can he choose his new suit? [2 APP
marks]
2) A Chinese restaurant features a lunch special with a choice of wonton soup, dumplings, or
spring roll to start, 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 specials at this restaurant. How
many different possibilities are there? [4 APP marks]
3) Express in the form nPr. [1 KU mark each]
a) 22 x 21 x 20 x 19 x 18 x 17
b)
99 x 98 x 97 x 96
4) Evaluate the following. [1 KU mark each]
10!
7!3!
a) 6!
b) 4!
c)
26!
22!
d) 9P5
c)
5x4x3
e)
P(11,7)
5) In how many ways can a set of nine books be arranged on a shelf so that volumes one, two
and three are beside one another? [2 APP marks]
6) In how many different ways can 12 people stand in line for a photograph if the tallest &
shortest person CAN NOT stand next to each other? [3 APP marks]
7) How many permutations are there of the following words: [2 KU marks each]
a) Function
b)
Calculus
8) Write out the first 5 rows of Pascal’s Triangle. (The 1st one represents row 0) [2 KU
marks]
9) The sum of the terms in the 8th row in Pascal’s Triangle is __________ [1 KU mark]
10) T17,14 + t17,15 simplified to a single term from Pascal’s Triangle is __________ [1 KU mark]
11) How many paths spell MICROWAVE? [2 KU marks]
M
I
C
R
O
I
C
R
O
W
C
R
O
W
A
R
O
W
A
V
O
W
A
V
E
12)
Nadia’s office is six blocks east and two blocks south of her house. Assume that she walks
only east or south when going from home to work. Determine how many different routes
Nadia can take. Draw a diagram. [4 APP marks]