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Permutations and combinations Practice for task 2

perms and combs practice
Subject

Maths Extension 1

138 Documents
Students shared 138 documents in this course
Degree • Grade

HSC

• 11
Academic year: 2022/2023
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Felix Mathew
Woolooware High School
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EXT 1: Combinatorics (Ext1), A1 Working with Combinatorics (Y11)

Permutations and Combinations (Ext1)

Teacher: Roy Leon Cruz Exam Equivalent Time: 49 minutes (based on HSC allocation of 1 minutes approx. per mark)

A1 Combinatorics

1% 2% 3% 4% 5% 6% 7%

Permutations and Combinations

Binomial Expansion

*Analytics based on the average contribution to the EXT1 HSC exams over the past decade.

HISTORICAL CONTRIBUTION

Combinatorics looks at counting and ordering techniques and introduces binomial coefficients within this context. This topic has been split into two sub-categories for analysis purposes which are: 1-Permutations and Combinations (3%) and 2-Binomial Expansion (3%). This analysis looks at Permutations and Combinations.

HSC ANALYSIS - What to expect and common pitfalls

Permutations and Combinations (3%) are examined every year, at least once.

Examiners have favoured the multiple choice format for this sub-topic, asking an MC question in 9 of the last 10 years (most recently in 2021). Most multiple choice questions have been of moderate difficulty, although 2018 8 MC deserves attention. Longer answer questions have been rare in recent years although they were included in 5 seperate exams between 2010-2015 , with allocations of 2-5 marks. Given the low mean marks of these questions and the fact that probability is no longer in the Ext2 syllabus, we highly recommend a revision focus here. The pigeonhole principle represents new Ext1 content whose importance is underscored by its inclusion in 2021 and 2020 exams where it caused problems on both occasions with mean marks of 31% and 52% respectively. These questions, along with Ext1 EQ-Bank Q12-14, should be included in any revision.

Be aware that this topic area is the source of some of the most difficult questions examiners have thrown at students (some of the beasts include 2015 Ext1 14c, 2014 Ext1 14b and 2010 Ext1 7c).

1. Combinatorics, EXT1 A1 2016 HSC 8 MC

2. Combinatorics, EXT1 A1 2012 HSC 5 MC

3. Combinatorics, EXT1 A1 2013 HSC 7 MC

Questions

A team of 11 students is to be formed from a group of 18 students. Among the 18 students are 3 students who are left-handed.

What is the number of possible teams containing at least 1 student who is left-handed? (A)

(B) (C)

(D)

How many arrangements of the letters of the word are possible if the and the are to be together in any order?

(A)

(B)

(C)

(D)

A family of eight is seated randomly around a circular table. What is the probability that the two youngest members of the family sit together?

(A)
(B)
(C)
(D)

4. Combinatorics, EXT1 A1 2014 HSC 8 MC

5. Combinatorics, EXT1 A1 2019 HSC 8 MC

6. Combinatorics, EXT1 A1 2018 HSC 8 MC

7. Combinatorics, EXT1 A1 2011 HSC 2e

In how many ways can 6 people from a group of 15 people be chosen and then arranged in a circle?

(A)
(B)
(C)
(D)

In how many ways can all the letters of the word PARALLEL be placed in a line with the three Ls together?

A.
B.
C.
D.

Six men and six women are to be seated at a round table. In how many different ways can they be seated if men and women alternate?

A.

B.

C.

D.

Alex’s playlist consists of 40 different songs that can be arranged in any order.

i. How many arrangements are there for the 40 songs? (1 mark) ii. Alex decides that she wants to play her three favourite songs first, in any order.

How many arrangements of the 40 songs are now possible? (1 mark)

8. Combinatorics, EXT1 A1 2004 HSC 2e

9. Combinatorics, EXT1 A1 2021 HSC 11d

10. Combinatorics, EXT1 A1 SM-Bank 11

11. Combinatorics, EXT1 A1 EQ-Bank 4

12. Combinatorics, EXT1 A1 EQ-Bank 14

13. Combinatorics, EXT1 A1 2012 HSC 11e

14. Combinatorics, EXT1 A1 2007 HSC 5b

A four-person team is to be chosen at random from nine women and seven men. i. In how many ways can this team be chosen? (1 mark) ii. What is the probability that the team will consist of four women? (1 mark)

A committee containing 5 men and 3 women is to be formed from a group of 10 men and 8 women. In how many different ways can the committee be formed? (1 mark)

A multiple choice quiz asks students 4 questions. Each question has three possible answers, a, b or c, and students must attempt each question. How many students must do the quiz to ensure that at least two sets of answers are identical? ( marks)

How many numbers greater than 6000 can be formed with the digits 1, 4, 5, 7, 8 if no digit is repeated. (2 marks)

A delivery company has 1095 packages to deliver on a given day.

It has 17 delivery vans that will deliver all packages. Find the minimum number of packages that at least one of the vans delivers. (2 marks)

In how many ways can a committee of 3 men and 4 women be selected from a group of 8 men and 10 women? (1 mark)

Mr and Mrs Roberts and their four children go to the theatre. They are randomly allocated six adjacent seats in a single row.

What is the probability that the four children are allocated seats next to each other? (2 marks)

♦ Mean mark 47%.

5. Combinatorics, EXT1 A1 2019 HSC 8 MC

♦ Mean mark 42%.

6. Combinatorics, EXT1 A1 2018 HSC 8 MC

7. Combinatorics, EXT1 A1 2011 HSC 2e

i.

ii.

8. Combinatorics, EXT1 A1 2004 HSC 2e

9. Combinatorics, EXT1 A1 2021 HSC 11d

COMMENT: Note that "By PHP" refers to by pigeonhole principle.

10. Combinatorics, EXT1 A1 SM-Bank 11

11. Combinatorics, EXT1 A1 EQ-Bank 4

i.

ii.

COMMENT: Note that "By PHP" refers to by pigeonhole principle.

12. Combinatorics, EXT1 A1 EQ-Bank 14

13. Combinatorics, EXT1 A1 2012 HSC 11e

14. Combinatorics, EXT1 A1 2007 HSC 5b

Mean mark 52%.

15. Combinatorics, EXT1 A1 2020 HSC 12c

19. Combinatorics, EXT1 A1 2008 HSC 4b

i.

ii.

Copyright © 2016-2022 M2 Mathematics Pty Ltd (SmarterMaths.com)

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Permutations and combinations Practice for task 2

Subject: Maths Extension 1

138 Documents
Students shared 138 documents in this course
Degree • Grade:

HSC

• 11
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EXT 1: Combinatorics (Ext1), A1 Working with Combinatorics (Y11)
Permutations and Combinations (Ext1)
Teacher: Roy Leon Cruz
Exam Equivalent Time: 49.5 minutes (based on HSC allocation of 1.5 minutes approx.
per mark)
A1 Combinatorics
1%
2%
3%
4%
5%
6%
7%
Permutations and Combinations
Binomial Expansion
*Analytics based on the average
contribution to the EXT1 HSC
exams over the past decade.
HISTORICAL CONTRIBUTION
Combinatorics looks at counting and ordering techniques and introduces binomial coefficients within
this context.
This topic has been split into two sub-categories for analysis purposes which are: 1-Permutations
and Combinations (3.4%) and 2-Binomial Expansion (3.6%).
This analysis looks at Permutations and Combinations.
HSC ANALYSIS - What to expect and common pitfalls
Permutations and Combinations (3.4%)are examined every year, at least once.
Examiners have favoured the multiple choice format for this sub-topic, asking an MC question in 9 of
the last 10 years (most recently in 2021).
Most multiple choice questions have been of moderate difficulty, although 2018 8 MC deserves
attention.
Longer answer questions have been rare in recent years although they were included in 5 seperate
exams between 2010-2015 , with allocations of 2-5 marks. Given the low mean marks of these
questions and the fact that probability is no longer in the Ext2 syllabus, we highly recommend a
revision focus here.
The pigeonhole principle represents new Ext1 content whose importance is underscored by its
inclusion in 2021 and 2020 exams where it caused problems on both occasions with mean marks of
31% and 52% respectively. These questions, along with Ext1 EQ-Bank Q12-14, should be included in
any revision.
Be aware that this topic area is the source of some of the most difficult questions examiners have
thrown at students (some of the beasts include 2015 Ext1 14c, 2014 Ext1 14b and 2010 Ext1 7c).
1.Combinatorics, EXT1 A1 2016 HSC 8 MC
2.Combinatorics, EXT1 A1 2012 HSC 5 MC
3.Combinatorics, EXT1 A1 2013 HSC 7 MC
Questions
A team of 11 students is to be formed from a group of 18 students. Among the 18 students are 3
students who are left-handed.
What is the number of possible teams containing at least 1 student who is left-handed?
(A) 
(B) 
(C) 
(D) 
How many arrangements of the letters of the word  are possible if the  and the
are to be together in any order?
(A) 
(B) 
(C)
(D)
A family of eight is seated randomly around a circular table.
What is the probability that the two youngest members of the family sit together?
(A) 
(B) 
(C) 
(D)

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