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11 Specialist Mathematics - Ch 7 Combinatorics

Total questions: 11

Worksheet time: 11mins

Name
Class
Date
1.

Bao plans to study six subjects in Year 12. He has already chosen three subjects and for the remaining three he plans to choose one of four languages, one of three mathematics subjects and one of four science subjects. How many ways can he select his remaining subjects?

a)

6

b)

11

c)

48

d)

165

e)

990

2.

There are three flights directly from Melbourne to Brisbane. There are also two flights from Melbourne to Sydney and then four choices of connecting flight from Sydney to Brisbane. How many different paths are there from Melbourne to Brisbane?

a)

9

b)

11

c)

18

d)

20

e)

24

3.

In how many ways can 10 people be arranged in a queue at the bank?

a)

10!

b)

1010

c)

210

d)

10C2

e)

10C1

4.

How many three-digit numbers can be formed using the digits 1, 2, 3, 4, 5 and 6 at most once?

a)

6C3

b)

3!

c)

6!

d)

6 x 5 x 4

e)

6 + 5 + 4

5.

How many permutations of the word UTOPIA begin and end with a vowel?

a)

90

b)

288

c)

384

d)

720

e)

4320

6.

How many ways can four identical red flags and three identical blue flags be arranged in a row?

a)

4 x 3

b)

7! / (4! x 3!)

c)

7! x 3! x 4!

d)

4! x 3!

e)

2! x 3! x 4!

7.

How many ways can three DVDs be chosen from a collection of nine different DVDs?

a)

3!

b)

9 x 8 x 7

c)

9C3

d)

9! / 3!

e)

3 x 9

8.

The number of subsets of {A,B,C,D,E,F} with at least one element is

a)

6C2

b)

6C2 - 1

c)

25 - 1

d)

26 - 1

e)

26

9.

A class consists of nine girls and eight boys. How many ways can a group of two boys and two girls be chosen?

a)

17! / (2! x 2!)

b)

17C4

c)

9C2 x 8C2

d)

17! / (9! x 8!)

e)

9 x 8 x 8 x 7

10.

There are six blue balls and five red balls in a bag. How many balls need to be selected at random before you are certain that three will have the same colour?

a)

3

b)

4

c)

5

d)

7

e)

11

11.

Each of the 30 students in a class studies French, German or Chinese. Of these students, 15 study French, 17 study German and 15 study Chinese. There are 15 students that study more than one subject. How many students study all three subjects?

a)

2

b)

3

c)

4

d)

5

e)

6