Difference between Permutation and Combination (h2 math)

MagnesiumOxide

16 Dec 12, 12:37

Hey guys I am really confused with the difference between P&C. I know that permutation has a certain fixed order but combination doesn't. But what exactly does this means? Some kind soul pls help ;)

SBS n SMRT

16 Dec 12, 13:18

Permutation means arrangement is important

Combination means any arrangement

E.g. 1,2,3,4,5, find the number of possible numbers to be formed if all must be used only once

This means that 12345 and 12354 is both counted as the arrangement is different

E.g. 5 students, 3 students to be a committee

Ans: 5C3 as we don't care whether the order of selection is Andy, Lucas, Tom or T,L,A or what, we just need to know which 3 students is the committee

BUT if 5 students, 3 must seat in a row, how many ways

Ans: 5P3 as the order is important now, as ALT and TLA is certainly different now

MagnesiumOxide

16 Dec 12, 13:30

Originally posted by SBS n SMRT:

Permutation means arrangement is important

Combination means any arrangement

E.g. 1,2,3,4,5, find the number of possible numbers to be formed if all must be used only once

This means that 12345 and 12354 is both counted as the arrangement is different

E.g. 5 students, 3 students to be a committee

Ans: 5C3 as we don't care whether the order of selection is Andy, Lucas, Tom or T,L,A or what, we just need to know which 3 students is the committee

BUT if 5 students, 3 must seat in a row, how many ways

Ans: 5P3 as the order is important now, as ALT and TLA is certainly different now

Oh I thnk I finally get it already. Thnks for explaining! :))

wee_ws

16 Dec 12, 13:30

Hi,

It is ok to feel a little confused since you are new to the topic.

Consider two situations:

1. Arrange 3 items out of 5 (say, a, b, c, d, e).

2. Select 3 items out of 5 (say, a, b, c, d, e).

Situation 1 is an instance of permutation (note the keyword 'arrange'). Situation 2 is an instance of combination (note the keyword 'select').

In situation 1, number of ways = 5 x 4 x 3 = 60.

In situation 2, number of ways = 5C3 = (5!) / [(3!)(2!)] = 10.

In situation 2, we are not interested in the order of the 3 items selected and we can list systematically the 10 possibilities as follow:

a, b, c
a, b, d
a, b, e
a, c, d
a, c, e
a, d, e
b, c, d
b, c, e
b, d, e
c, d, e

In situation 1, order matters, say, when we arrange the 3 items a, b, c. This could be done in 6 ways:

a, b, c
a, c, b
b, a, c
b, c, a
c, a, b
c, b, a

Thanks.

Cheers,
Wen Shih

SBS n SMRT

16 Dec 12, 13:33

PnC is one of the most irritating topic I agree, as it is either a 4m or 0m case. Usually with practice maths become easier but it is not for PnC. Understanding concepts is very important, so do look through the notes carefully and read questions very carefully. I lost about 4marks this A levels just seeing the question wrongly.

PnC is about using the correct tool (method) to solve the questions, so not one method will work with all the questions. Do be familiar with slotting in method as well as exclusion method ("complement") case and when to use which one.

SBS n SMRT

16 Dec 12, 13:34

Originally posted by wee_ws:

Hi,

It is ok to feel a little confused since you are new to the topic.

Consider two situations:

1. Arrange 3 items out of 5 (say, a, b, c, d, e).

2. Select 3 items out of 5 (say, a, b, c, d, e).

Situation 1 is an instance of permutation (note the keyword 'arrange'). Situation 2 is an instance of combination (note the keyword 'select').

In situation 1, number of ways = 5 x 4 x 3 = 60.

In situation 2, number of ways = 5C3 = (5!) / [(3!)(2!)] = 10.

In situation 2, we are not interested in the order of the 3 items selected and we can list systematically the 10 possibilities as follow:

a, b, c
a, b, d
a, b, e
a, c, d
a, c, e
a, d, e
b, c, d
b, c, e
b, d, e
c, d, e

In situation 1, order matters, say, when we arrange the 3 items a, b, c. This could be done in 6 ways:

a, b, c
a, c, b
b, a, c
b, c, a
c, a, b
c, b, a

Thanks.

Cheers,
Wen Shih

Important Note to add on, remember to divide by the prime (!) of the number of identical objects as they are indistinguishable (i.e. 5C3 = (5!) / [(3!)(2!)] = 10.)

SBS n SMRT

16 Dec 12, 13:35

Originally posted by MagnesiumOxide:

Oh I thnk I finally get it already. Thnks for explaining! :))

Welcomed ... :)))

MagnesiumOxide

16 Dec 12, 13:39

Originally posted by wee_ws:

Hi,

It is ok to feel a little confused since you are new to the topic.

Consider two situations:

1. Arrange 3 items out of 5 (say, a, b, c, d, e).

2. Select 3 items out of 5 (say, a, b, c, d, e).

Situation 1 is an instance of permutation (note the keyword 'arrange'). Situation 2 is an instance of combination (note the keyword 'select').

In situation 1, number of ways = 5 x 4 x 3 = 60.

In situation 2, number of ways = 5C3 = (5!) / [(3!)(2!)] = 10.

In situation 2, we are not interested in the order of the 3 items selected and we can list systematically the 10 possibilities as follow:

a, b, c
a, b, d
a, b, e
a, c, d
a, c, e
a, d, e
b, c, d
b, c, e
b, d, e
c, d, e

In situation 1, order matters, say, when we arrange the 3 items a, b, c. This could be done in 6 ways:

a, b, c
a, c, b
b, a, c
b, c, a
c, a, b
c, b, a

Thanks.

Cheers,
Wen Shih

So we just look at the keywords in the question?

If the question says select 3 balls out of 6 distinct balls , and arrange them in a row, then we will apply both? :)

MagnesiumOxide

16 Dec 12, 13:46

Originally posted by SBS n SMRT:

PnC is one of the most irritating topic I agree, as it is either a 4m or 0m case. Usually with practice maths become easier but it is not for PnC. Understanding concepts is very important, so do look through the notes carefully and read questions very carefully. I lost about 4marks this A levels just seeing the question wrongly.

PnC is about using the correct tool (method) to solve the questions, so not one method will work with all the questions. Do be familiar with slotting in method as well as exclusion method ("complement") case and when to use which one.

Ya!! Haha actually I have almost completed my tutorial on p&c already but will still get confused between those 2 formulas sometimes.. Guess I have to read thru examples in notes again. Lol

MUFC

16 Dec 12, 14:40

Originally posted by MagnesiumOxide:

So we just look at the keywords in the question?

If the question says select 3 balls out of 6 distinct balls , and arrange them in a row, then we will apply both? :)

This sounds like 6P3 to me. Arranging the balls in a row implies that the order is important. Let me label the balls A, B, C, D, E, F (since they are distinct). Suppose I try to select 3 balls at random and I get B, C, D. Then I am supposed to arrange them in a row, and there are several ways to do so, eg BCD or BDC or DBC. 6P3 takes care of the number of ways of selecting the 3 balls and arranging them in a row.

You may want to note that 6P3 is equivalent to 6C3 x 3! . 6C3 represents choosing the balls without caring about the order first, and 3! is the number of ways you can arrange those 3 balls in a row. You can write 6P3 or 6C3 x 3! as your answer and both should be accepted =)

Seowlah

16 Dec 12, 15:17

Originally posted by MagnesiumOxide:

Hey guys I am really confused with the difference between P&C. I know that permutation has a certain fixed order but combination doesn't. But what exactly does this means? Some kind soul pls help ;)

Permutation is for winning 4D ie 4 digits must be in the exact order.

Combination is for winning Toto ie 6 numbers can be in any order.

MagnesiumOxide

16 Dec 12, 18:57

Originally posted by MUFC:

This sounds like 6P3 to me. Arranging the balls in a row implies that the order is important. Let me label the balls A, B, C, D, E, F (since they are distinct). Suppose I try to select 3 balls at random and I get B, C, D. Then I am supposed to arrange them in a row, and there are several ways to do so, eg BCD or BDC or DBC. 6P3 takes care of the number of ways of selecting the 3 balls and arranging them in a row.

You may want to note that 6P3 is equivalent to 6C3 x 3! . 6C3 represents choosing the balls without caring about the order first, and 3! is the number of ways you can arrange those 3 balls in a row. You can write 6P3 or 6C3 x 3! as your answer and both should be accepted =)

Ohh! I finally get it now! Hahaa thanks alot for your detailed explaination!! :))

MagnesiumOxide

16 Dec 12, 19:07

Originally posted by Seowlah:

Permutation is for winning 4D ie 4 digits must be in the exact order.

Combination is for winning Toto ie 6 numbers can be in any order.

LOL nice one :DDD

wee_ws

16 Dec 12, 19:21

Hi,

Be sure to be able to deal with these types of questions that have appeared in past years' exams (2007 - 2012):

- arrangement of people in a line and circle;

- selection of people to form groups;

- arrangement of letters;

- arrangement of digits (with probability assessed at the same time);

- selection of an arbitrary number of people (with probability and inequalities assessed at the same time);

- arrangement of people in a line and circle (with probability assessed at the same time).

Cambridge-set questions are much more manageable than school-based ones.

Thanks!

Cheers,
Wen Shih

MagnesiumOxide

16 Dec 12, 19:27

Originally posted by wee_ws:

Hi,

Be sure to be able to deal with these types of questions that have appeared in past years' exams (2007 - 2012):

- arrangement of people in a line and circle;

- selection of people to form groups;

- arrangement of letters;

- arrangement of digits (with probability assessed at the same time);

- selection of an arbitrary number of people (with probability and inequalities assessed at the same time);

- arrangement of people in a line and circle (with probability assessed at the same time).

Cambridge-set questions are much more manageable than school-based ones.

Thanks!

Cheers,
Wen Shih

Ok noted!:) will keep a look out for these questions! Thanks once again! =)))

SBS n SMRT

16 Dec 12, 19:31

Originally posted by wee_ws:

Hi,

Be sure to be able to deal with these types of questions that have appeared in past years' exams (2007 - 2012):

- arrangement of people in a line and circle;

- selection of people to form groups;

- arrangement of letters;

- arrangement of digits (with probability assessed at the same time);

- selection of an arbitrary number of people (with probability and inequalities assessed at the same time);

- arrangement of people in a line and circle (with probability assessed at the same time).

Cambridge-set questions are much more manageable than school-based ones.

Thanks!

Cheers,
Wen Shih

disagree for 2012 :( so difficult

MagnesiumOxide

16 Dec 12, 19:59

Originally posted by SBS n SMRT:

disagree for 2012 :( so difficult

Hope next year's p&c will be manageable.. Haha!

MUFC

17 Dec 12, 00:39

My opinion is to do enough practice so that you have a good overview of the different kinds of questions that may come out and the methods to solve them, but not to spend so much time on this topic that you end up neglecting other topics. Even the best students struggle with this topic and very few students are 100% sure of their answers. Leave a certain detail out and your answer would be wrong.

charlize

17 Dec 12, 00:46

Originally posted by Seowlah:

Permutation is for winning 4D ie 4 digits must be in the exact order.

Combination is for winning Toto ie 6 numbers can be in any order.

Some people will find using this as a base to start more clearer than using red balls or blue balls.

^Acid^ aka s|aO^eH~

17 Dec 12, 09:25

Originally posted by Seowlah:

Permutation is for winning 4D ie 4 digits must be in the exact order.

Combination is for winning Toto ie 6 numbers can be in any order.

Seriously... That's wat I always tell my friends

Seowlah

17 Dec 12, 22:02

Permutation is for winning for 4D.

How many tickets to buy to sure win ? 10^4 = 10000 tickets

Visualise the joy when you see that you win all the prizes in the draw

But you will lose $3000 plus

Combination is for winning for Toto

How many tickets to buy to sure win ? 45C6 = 8145060 tickets.

Visualise the joy when you see that you win all the prizes in the draw

But you will only win money during the Chinese New Year HongBao Draw and there are only two winners.

M the name

17 Dec 12, 22:35

Originally posted by Seowlah:

Permutation is for winning for 4D.

How many tickets to buy to sure win ? 10^4 = 10000 tickets

Visualise the joy when you see that you win all the prizes in the draw

But you will lose $3000 plus

Combination is for winning for Toto

How many tickets to buy to sure win ? 45C6 = 8145060 tickets.

Visualise the joy when you see that you win all the prizes in the draw

But you will only win money during the Chinese New Year HongBao Draw and there are only two winners.

Then what is the winning odd of Permutation and Combination for Singapore Sweep, Slot Machine and Bingo ? *'@^@||| dizzy

Seowlah

17 Dec 12, 23:13

Permutation is for winning Singapore Sweep.

How many tickets to buy to sure win ? 3 x 10^6 = 3000000 tickets.

Visualise the joy when you see that you win all the prizes in the draw.

But you will lose $3,000,000 plus in the fifth Super Sweep Snowball draw The loss is too huge

Calculations for jackpot machines and bingo are more complex.

PS : Expected value is used to determine whether a gambling game is fair or unfair.

All gambling games in casinos are unfair ie the expected value of the games are always in favour to the casino owners

charlize

18 Dec 12, 00:22

Yes, casino games all have negative expectancy for the players.

Seowlah

18 Dec 12, 01:01

How does the logic of a jackpot machine work ?

A simple jackpot machine has 3 fruits apples, bananas and cherries

To pay $0.01 to play the game once

To win $1 when 3 apples appear in a row

Do you wish to play the game ?

Will you win or lose money in playing the game ?

It will depend how often the casino allow the 3 apples to appear in a row.

A random number generator and a set of secret alogorithm is used to determine when the 3 apples will appear in a row.