Tricks in permutation and cominations (1 Viewer)
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Definitely one of the hardest topics and still at the forefront of the NESA test writers’ minds (as indicated by the last question of the 2020 Ext 1 HSC) despite being a Yr11 topic. What makes this topic so hard is the very fact that you can be asked anything. However, when doing it you begin to find that a lot of the questions are different variations of the same thing. So my advice to you would be to make a note of these standard question types and how to solve them. After this, look at as many niche questions as possible (in past papers) and try to solve them yourself then look at the marking guideline’s approach. There are some specialised techniques you can pick up in these questions. As a general tip I would try to break down a question into simpler cases which you can then solve for. Hope this helps!
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tickboom
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I agree, permutation and combinations is hard! Even at uni I did a subject called Combinatorial Probability and it was one of the toughest subjects of the whole Actuarial Studies degree! I also agree that nothing beats practicing the broadest range of questions possible. These questions don't really have a rigid formulaic approach to them, so the best you can do is hope that anything you encounter on an exam is something you've already been exposed to.
This is one area where pausing to think can save you a lot of time, rather than just diving in to the questions... and remember, if the question is only worth a couple of marks and the approach that you are considering will take a couple of pages, think again. A long answer is better than no answer, but a short answer is better still... so only do the long way if you have the time and you are confident you can get the answer.
Whilst I agree there is a lot of variation most of perms and combs is formulaic just like the rest of the syllabus (by most I mean like 80% whereas 20% is unknown or has a trick). You will find a lot of questions use the same trick whereas a few require you to try something new.
Thats true, as i do alot of questions i see that there are alot of variation
Would an example being using tree diagram instead of multiplication and addition principal
That is so correct, as i do the questions, i can see that there is very little change, although, how do i counter the proof questions, those tend to be harder
Give an example.
What do you mean in particular? Could you provide an example?
Eagle Mum
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I thought they were essentially the same process. When you draw a tree diagram, you multiple the probabilities of consecutive events along each branch, then you add the final products of the branches that fit the stated conditions/outcomes.
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I was thinking of a question like:
Consider the "words" that can be made by rearranging the letters of MATHEMATICS. How many different words can be made in which the "S" occurs before the "H"?
Well the “S” can occur either before or after the “H” making the probability 1/2.
Sorry misread! It’s not a probability question. Oops!
Then it becomes 11!/(2x2!x2!x2!).
Haha I have made that mistake a few times!
Correct.
The long way is to try to count all the options with the S before the H... and it is a lot longer than your solution.
How did you get this answer?, the only way i can think off getting this is by listing out all the options for S behind H. I am super confused rn
Half the total ways are when S is to the left of H and half are when S is to the right of A. So simply work out the total number of ways of arranging the letters in general then divide by 2 (what Bianca did).
Can't say I'm great at Perms and Combs, but most of what is important has been mentioned above. Some few general pointers are:
- Recognise whether the question is a permutation (a situation where order matters) or a combination (a situation where order does not matter). An example of a permutation would be "How many ways can you choose 10 people for a Treasurer, Accountant and Leader?" as each role is different and the order does matter. Likewise, an example of a combination would be "How many ways can you select 3 men and 2 women out of 6 men and 7 women?" as the order does not matter.
Like what someone above me said, try and remember each of the typical forms of questions the examiners would throw at you.
- Try and understand both the nCr/nPr notation and factorial notation. In questions involving proving binomial identities it will sometimes be easier to work in factorial notation rather than the nCr/nPr notation or vice versa. Chances are you'll probably attempt at least one of these kinds of questions between now and the end of next year, whether it be in a class test, a textbook exercise or in the HSC paper (i.e that one question from the 2020 exam).