rodger159 Posted November 19, 2011 Posted November 19, 2011 Hey, been given a few questions, done most of them but have no idea how to even start this, I would go to a lecturer but I feel it needs doing before then. Question: A particular lottery has the following rules: - you choose 5 numbers, with no repeats, from 34 numbers. -you then choose an additional bonus number from 14 numbers. This step does not depend on how you choose the first numbers. -To win the jackpot, your first five numbers must match the first five numbers drawn from 34, in any order, AND your bonus number must match the one drawn from 14. If you wanted to be guaranteed to win this lottery jackpot, what is the minimum number of tickets you would need to purchase? I thought first one would have been C(34, 5) but that just gives massive numbers back, and C(14,1) for the second but no idea how these would even link up. How would I even go about starting this? Thanks. Accidentally put this in the homework section without realising there is a computer science section, sorry.
Xittenn Posted November 19, 2011 Posted November 19, 2011 35 nCr 5 = 324632 This is a big number??? Looks right to me Lotto 6/49 odds are 49 nCr 6 = 13983816 which is what is claimed to be the odds of winning the jackpot. I'm sure you know how to AND the bonus number in as well . . . . . When I'm unsure about something like this I review the concept so that I become sure. There is nothing worse than getting into an exam or something and freaking out because you can't quite remember straight. Just sayin'!
rodger159 Posted November 19, 2011 Author Posted November 19, 2011 35 nCr 5 = 324632 This is a big number??? Looks right to me Lotto 6/49 odds are 49 nCr 6 = 13983816 which is what is claimed to be the odds of winning the jackpot. I'm sure you know how to AND the bonus number in as well . . . . . When I'm unsure about something like this I review the concept so that I become sure. There is nothing worse than getting into an exam or something and freaking out because you can't quite remember straight. Just sayin'! factorial of 34 / factorial 5 * factorial 29 gives me the the answer: 8841761993739701954543616000000 for the first part. Surly not?!
Xittenn Posted November 19, 2011 Posted November 19, 2011 Ooops I did 35 . . . . . . [math] \frac{34!}{5!29!} = \frac{2.95232799E38}{120(8.841761994E30)} = 278256 [/math] Why not use the nCr function of your calculator? What calculator are you using?
rodger159 Posted November 19, 2011 Author Posted November 19, 2011 No idea what you mean by the nCr function. Just the windows one at the moment. Haven't got around to buying a proper one, can't even find the E button on the windows one?!
Xittenn Posted November 19, 2011 Posted November 19, 2011 You can do 34 nCr 5 with Wolfram Alpha. On a TI-83 the nCr function is [MATH][PRB][3] . . . . . As I recall a decent downloadable freeware calculator is currently not available. Maybe one day I'll have one I can link, but regardless, Wolfram Alpha does everything and then some.
rodger159 Posted November 19, 2011 Author Posted November 19, 2011 I'm awful at maths and having an poor lecturer to add to that doesn't make things much better. Ah thanks, I'll have to make sure I get a decent calculator with that button on. Never knew you could do that, I'm assuming nCr just means work out the combination? and nPr for the permutations? As 14 nCr 1 is 14 would timing them together give the answer? As in 278256 * 14 = 3895584
Xittenn Posted November 19, 2011 Posted November 19, 2011 Yes, nCr is combinations and nPr is permutations. Anything that is 'AND' is a multiplication and anything that is 'OR' is addition. These are basics of math that you are most definitely going to want to become familiar with.
rodger159 Posted November 19, 2011 Author Posted November 19, 2011 Ah well that should be it then! Thanks for your help! So much for "yeah there wont be much maths if you start computer science here" BAM, books full of it.
imatfaal Posted November 20, 2011 Posted November 20, 2011 Rodger - you can always do calculation such as 34!/29! on the windows calcultor - or even on paper, and you should be able to get a fair approximation in your head. Bear in mind if you wrote it out in full you would cancel from top and bottom every number 29 and under 34*33*32*31*30*29*28*..... --------------------------------- 29*28*27*.... after cancellation ends up as 34*33*32*31*30 - now this number is never gonna be close to your 31 digit number, and will be even smaller when divided by 120. I have to be very cautious with my maths, as I really don't get it intuitively, and double checking that your results are in the right ball park (orders of magnitude) is a very good way to start. The windows calculator has two"views" standard and scientific xy is only available in scientific
rodger159 Posted November 20, 2011 Author Posted November 20, 2011 I think in all exams we will have a calculator mind, and I cant see myself ever needing to work it out without a calculator in life But thanks! Double checking answers is always a good idea, but when I can simply key the numbers into a calculator along with the nCr and nPr it shouldn't be a problem anyway.
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