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Thread: Combinatorics

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    Junior Member _Anonymous's Avatar
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    Combinatorics

    I'm not really a fan of Perms and Combs. The questions are very unpredictable and I tend to struggle with the mechanisms on going through and solving the problems. Sadly, it'll still be tested every time we encounter the topic and I want to to know how people go about solving these questions. How do you deal with restrictions, how do you decipher the question? How do you know your answer is right (which is a major problem with this topic, since you can't really check your answer unlike most other topics)?

    And lastly, how hard does the topic get in Year 12? I know that Binomial theorem goes over this, but how much harder does it get?

    Is this a huge topic in the HSC exams? Or is it more Calculus based?

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    Junior Member HeroWise's Avatar
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    Re: Combinatorics

    Im no way in year 12 to decide on the state of perms and combs. Tbh i really love the topic. The problem here is understanding of the questions. Yes I do agree with you about the unpredictability of this topic. I believe this is one topic that ONLY practice wont make you better. You do a wide range of questions (You may find MANY repetitions with the questions) and still get through ur exams. In my honest opinion, please dont judge, I believe that you need to understand year 10 probability back to front. IF that is solid, then you will understand the nature of probabilty and hence really help you in perms and combs. Have a crack at those cambridge questions, they really do solidify ur understanding. Try the HARD questions rather than the easy ones because thats where you will understand the topic more and perhaps appreciate it too.

    I know that you cant be asked hard perms and combs qtn in 3u. BUt in 4u harder 3u, u got perms and combs and they can be asked in certain ocassions.

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    Junior Member _Anonymous's Avatar
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    Re: Combinatorics

    Quote Originally Posted by HeroWise View Post
    Im no way in year 12 to decide on the state of perms and combs. Tbh i really love the topic. The problem here is understanding of the questions. Yes I do agree with you about the unpredictability of this topic. I believe this is one topic that ONLY practice wont make you better. You do a wide range of questions (You may find MANY repetitions with the questions) and still get through ur exams. In my honest opinion, please dont judge, I believe that you need to understand year 10 probability back to front. IF that is solid, then you will understand the nature of probabilty and hence really help you in perms and combs. Have a crack at those cambridge questions, they really do solidify ur understanding. Try the HARD questions rather than the easy ones because thats where you will understand the topic more and perhaps appreciate it too.

    I know that you cant be asked hard perms and combs qtn in 3u. BUt in 4u harder 3u, u got perms and combs and they can be asked in certain ocassions.
    Thanks for your reply. We never went through probability in Year 10 because we ran out of time and finished with Functions. I'd like to go over the topic but I don't really have time at all since my Yearlies are on at the moment. I attempt the hard Cambridge 3U questions from the Year 12 book (since it contains Perms and Combs questions) but struggle. I'll keep on doing more questions though, at least familiarise myself with the layouts. But how does one deal with restrictions and understanding the main question itself? Probably a stupid question, but oh well.

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    Re: Combinatorics

    Quote Originally Posted by _Anonymous View Post
    Thanks for your reply. We never went through probability in Year 10 because we ran out of time and finished with Functions. I'd like to go over the topic but I don't really have time at all since my Yearlies are on at the moment. I attempt the hard Cambridge 3U questions from the Year 12 book (since it contains Perms and Combs questions) but struggle. I'll keep on doing more questions though, at least familiarise myself with the layouts. But how does one deal with restrictions and understanding the main question itself? Probably a stupid question, but oh well.
    I think give us some questions we'll try explain our thought process.
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    Junior Member HeroWise's Avatar
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    Re: Combinatorics

    As pika said, send in questions nad we will try our best to show our thought process. The restrictions are weird smtms i do agree.

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    Junior Member _Anonymous's Avatar
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    Re: Combinatorics

    1) In how many ways can a committee of three women and four girls be chosen from seven women and
    six girls so that if the eldest woman is serving on the committee then the youngest girl is not?

    2) In how many ways can eight different toys be divided into two unequal groups? (this one seems easy and probably is, but what do we do about the unequal groups part?)

    3)The ratio of the number of combinations of (2n + 2) different objects taken n at a time to the number of
    combinations of (2n − 2) different objects taken n at a time is 99 : 7. Find the value of n.

    A team of 11 is chosen from 15 cricketers. Five of the 15 cricketers are bowlers only, two are wicketkeepers
    only and the rest are batters only. How many possible teams can be chosen that contain:
    (a) 4 bowlers, 1 wicketkeeper and 6 batters
    (b) at least 4 bowlers and at least 1 wicketkeeper?

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    Junior Member HeroWise's Avatar
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    Re: Combinatorics

    Ill do the first question,


    In my head i can think oof two cases, one where the elder is in and the other where she is not in and its normal.

    Case 1) Eler is in :

    |_| _ _ _ _ _ _

    The |_| is where the elder is so whe MUST be there thats possible in only one way
    now out of 7 there are 6 women, we do 6C2 and the youngest girl mus not be in it. There fore total of 5 girls to select from.

    so we have (6C2)(5C4)

    Case 2) Exclude elder
    7-1 woman so 6 woman choose 3 and from 6 girls choose 4

    (6C3)(6C4)



    Add them because they are two different possibilities:

    (6C2)(5C4)+(6C3)(6C4)

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    Member BenHowe's Avatar
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    Re: Combinatorics

    Pika see if you can do this with 212 stuff like partition theorem or generating functions
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    Re: Combinatorics

    imho you haven't been taught permutations and combinations properly. the questions ARE very predictable, and you CAN learn this topic. There are specific archetypes that repeat all the time.

    Yes, you do have some extremely hard questions, but you can say the same for every other topic too. The thing is, 99% of questions you'll come across in 3u maths for perms and combs ARE extremely easy and are absolutely predictable.

    Try to learn perms/combs by thoroughly understanding and learning the following types of questions:

    Basic Counting Theorem aka Multiplication Principle
    Ordered Selections with Repetition.
    Ordered Selections without Repetition.
    Permutations around a circular table
    Permutations with repeated/identical elements
    Permutations with Conditions - Groups
    Permutations with Conditions - Separation
    Permutations with Conditions - Complementary events (+ learn when to use separation instead)
    Permutations with Conditions - Other including cases
    Combinations - Basic
    Harder Combinations - Multiple cases, Multiple Groups, Successive Groups
    Harder Combinations: Selection of Groups of Identical Sizes (mostly 4u here tbh - check terry lee 4u)
    Algebraic questions involving nPr and nCr

    Imho (-very humble-) there are no textbooks which teach this topic well, unfortunately.
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    Re: Combinatorics

    Roy G Biv
    What evidence do you have that he hasn't been taught properly, vs hasn't learned it properly?

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    Junior Member HeroWise's Avatar
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    Re: Combinatorics

    I think he is referring generally like the topic is explained really well in schools and hence causes issues when dealing with hard questions. Schools show some basic fundamental archetypes which are what comes repeatedly in exams. But in harder 3u, u have more wider scope of perms and combs which involves derrangements etc, and i have heard many schools dont even touch it

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    Junior Member _Anonymous's Avatar
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    Re: Combinatorics

    Quote Originally Posted by Roy G Biv View Post
    imho you haven't been taught permutations and combinations properly. the questions ARE very predictable, and you CAN learn this topic. There are specific archetypes that repeat all the time.

    Yes, you do have some extremely hard questions, but you can say the same for every other topic too. The thing is, 99% of questions you'll come across in 3u maths for perms and combs ARE extremely easy and are absolutely predictable.

    Try to learn perms/combs by thoroughly understanding and learning the following types of questions:

    Basic Counting Theorem aka Multiplication Principle
    Ordered Selections with Repetition.
    Ordered Selections without Repetition.
    Permutations around a circular table
    Permutations with repeated/identical elements
    Permutations with Conditions - Groups
    Permutations with Conditions - Separation
    Permutations with Conditions - Complementary events (+ learn when to use separation instead)
    Permutations with Conditions - Other including cases
    Combinations - Basic
    Harder Combinations - Multiple cases, Multiple Groups, Successive Groups
    Harder Combinations: Selection of Groups of Identical Sizes (mostly 4u here tbh - check terry lee 4u)
    Algebraic questions involving nPr and nCr

    Imho (-very humble-) there are no textbooks which teach this topic well, unfortunately.
    Would you recommend a particular textbook where the questions generally are better for Perms and Combs? Some people recommend Cambridge, others Terry Lee and some also recommend Fitzpatrick for this topic. What do you think is a good book which has hard questions and is the most similar to the HSC questions for Perms and Combs?

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    Junior Member HeroWise's Avatar
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    Re: Combinatorics

    If u want most similar to HSC imo Fitz but if u want to get better at topic terry and camb
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