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Looking at 'their' solution, the question has not been specified well enough. Their solution assumes that cards of the same colour are otherwise distinguishable, and that is not evident from the wording. I would have interpreted the wording as the cards being distinguished only by colour...

Adding the three vectors is not enough. You have to guarantee any linear combination of the vectors will never be zero for them to be linearly independent. ie. can you find c1, c2, c3 for which c1(0, -5, 1) + c2(3, 4, -5) + c3(2, 1, -3) is zero?

Re: HSC 2015 3U Marathon [part b] Given that the batch is accepted, find the probability that more than 10% of the batch is defective

(a) 5^5 (b) 5! (c) 5 choices for the brother and sister, times 4^3 choices for the others

1 symbol: 2 possibilities 2 symbols: 2^2 = 4 possibilities 3 symbols: 2^3 = 8 possibilities . . . 10 symbols: 2^10 = 1024 possibilities Summing the GP: 2047 possibilities

Re: HSC 2015 4U Marathon I guess it depends on how visual a thinker someone is. For me, I find visual solutions much easier (and much more satisfying) than pure algebraic solutions. And I wouldn't be prepared to label someone a 'maths wiz' until they can visualize these kinds of things.

Nothing a little late night liver lubrication won't fix.

Re: HSC 2015 4U Marathon I didn't mention a region. I referred to the INTERVAL between (-2,0) and (2,0). There is no need to combine the arguments. It is MUCH easier to visualize rather than doing algebra. It is simply a case of playing with vectors. Try experimenting with different...

He actually DID differentiate the first one correctly, although something went wrong with the simplification. But yes, there is a definite weakness there in the algebraic skills.

Re: HSC 2015 4U Marathon The interval between (-2,0) and (2,0), and the entire y-axis (given that pi is the same as -pi)

Re: HSC 2015 3U Marathon "Dodge" in what way?

Re: HSC 2015 3U Marathon This is the probability that one SPECIFIC meal is not chosen, and one SPECIFIC person has the same meal as someone else.

Re: HSC 2015 3U Marathon My solution doesn't allow for 4 meals per diner. The fact that I am assigning diners to meals precludes that possibility. Each diner gets the one meal they are assigned to.

Re: HSC 2015 3U Marathon I'm having difficulty understanding your explanation. The first 5/6 seems to be randomly placed in the middle of a sentence ... I can't work out what you are doing with it. And you will have to explain who 'they' is ... do you mean the last person making a choice ...

Re: HSC 2015 3U Marathon Assign diners to meals (not meals to diners). The only way this scenario can occur is if 4 meals are chosen by exactly 1 person, 1 meal is chosen by 2 people, 1 meal is chosen by no-one. Select the meals which are to be chosen by 0 or 2 people ... 6P2 ... order...

Re: HSC 2015 3U Marathon I believe this is the correct answer. My calculation: 6P2 × 6C2 × 4! / (6⁶)

I still wonder where people come up with this nonsense.

Yeah, because being rich equates to having a high IQ? Like Britney Spears?

And I'm sure all one would need to do is draw a right-angled triangle with sides labelled appropriately to justify the use of those formulae. Just something that indicates they know where the formulae come from.

Re: HSC 2015 4U Marathon Why did you need the 'coprime' ?