Math 3201
Name: ___________________________
Unit 2 Test – Counting Methods
Formulae:
n!
 n  r !
P 
n r
n
 n
n!
Cr    
 r   n  r !r !
n!
a! b ! c !...
Part 1: Multiple Choice (11 marks)
Write the UPPERCASE letter of the correct answer in the correct blank on page 3.
1. Samantha is choosing an outfit to wear to the dance. She has 3 different tops, 4 different pants and
2 different pairs of shoes to choose from. How many different outfits could she make from this
selection of clothes?
A) 9
B) 12
C) 14
D) 24
2. Simplify:
A)
(n  2)!
n!
1
n  3n  2
2
B) 2!
C) 2n  3
D) n2  3n  2
3. How many ways can 8 friends stand in a row for a photograph if Molly, Krysta and Simone always
stand together?
A)
B)
C)
D)
1440
2160
4320
5040
1
4. Suppose a word is any string of letters. How many three-letter words can you make from the
letters in REGINA if you do not repeat any letters in the word?
A)
B)
C)
D)
16
20
120
216
5. How many different arrangements can be made using all the letters in NUNAVUT?
A)
B)
C)
D)
630
1260
2520
5040
6. The student council has 10 members, 6 girls and 4 boys. A dance committee is to be formed
consisting of exactly two girls and two boys. Which calculation could be used to determine the
number of different ways this committee could be formed?
A) 6 C2  4 C2
B) 6 P2  4 P2
C) 10 C4
D) 10 P4
7. A child going on a trip is told that out of his 8 favourite toys, he can bring at most three toys. How
many ways can be select the toys he brings?
A)
B)
C)
D)
8P0
+ 8P1 + 8P2 + 8P3
8C0 + 8C1 + 8C2 + 8C3
8C3 – (8C0 + 8C1 + 8C2)
8C0 × 8C1 × 8C2 × 8C3
8. Calculate:
A)
B)
C)
D)
6
 
 2
3
15
24
30
2
9. Solve for n:
A)
B)
C)
D)
 n  1!  12
 n  2 !
-13
11
12
13
10. How many different routes are there from A to B, if you only travel south or east?
A)
B)
C)
D)
28
112
360
1440
11. A combination lock opens with the correct three-digit code. Each wheel rotates through the digits 1 to
8. Which expression can be used to determine how many different three-digit codes are possible?
A)
P
8 3
B)
8
C) 8  7  6
C3
Selected Response Answer Sheet
1. ___
7. ___
2. ___
8. ___
3. ___
9. ___
4. ___
10. ___
5. ___
11. ___
6. ___
3
D) 8  8  8
Part 2: Constructed Response
Complete each question in the space provided. Show ALL workings to receive full marks.
11. A group of five Art Club students are to be selected for a field trip to The Rooms. If there are 6
boys and 7 girls in the Art Club, how many ways can the teacher select the five students if there
must be at least 3 girls?
[4 marks]
12. Algebraically solve for n:
P  72
[4 marks]
n1 2
4
13. Algebraically solve for n:
(n  6)!
 56
(n  4)!
[4 marks]
14. A) How many ways can you arrange the letters of the word MARVELOUS if each letter is used only
once? [1 mark]
B) Using the letters in the word MARVELOUS, how many 5 – letter “words” can be made which
consist of two vowels and three consonants? [2 marks]
5