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HSC 2016 MX1 Marathon (archive) (1 Viewer)

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leehuan

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Re: HSC 2016 3U Marathon

I don't understand how to do this.
A form has ten questions in order, each of which requires the answer 'Yes' or 'No'. Find the number of ways the form can be filled in:
(g) if exactly three answers are 'Yes', and they occur together,
_ _ _ _ _ _ _ (_ _ _)
The 3 yes's are always together, so we arrange them as one quantity (let's call it y). Note that the only possible ways of arranging (Y Y Y) in a line is 1.

N N N N N N N y
This is now a typical arrangement (making 'words'). Traditionally, the answer here is now 8!/(7!) = 8 ways.
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Alternatively, using stars and bars there is obviously 8 ways of doing so, because you have 7 bars (the no's) and only have to arrange one star (the y) anywhere between them or outside them.
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It's quite easy to check this. If we just list all the outcomes out, they are
Y Y Y N N N N N N N
N Y Y Y N N N N N N
N N Y Y Y N N N N N
N N N Y Y Y N N N N
N N N N Y Y Y N N N
N N N N N Y Y Y N N
N N N N N N Y Y Y N
N N N N N N N Y Y Y
Total: 8 ways
 

Drsoccerball

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Re: HSC 2016 3U Marathon

The answers a) 57 b)4days 8hrs

Sent from my D6503 using Tapatalk
2(7+6+5+...+1)+1 = total matches

57/12 = length of competition (Assuming they minimise time of tournament)
 

leehuan

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Re: HSC 2016 3U Marathon

This is what I got...



 

leehuan

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Re: HSC 2016 3U Marathon





NEXT QUESTION:
Ok, let's see how many 3U students will get thrown off by this...



















As the question is long, feel free to only answer a few parts of it. However, don't hog all the easy parts like (c).
 
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kawaiipotato

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Re: HSC 2016 3U Marathon





NEXT QUESTION:
Ok, let's see how many 3U students will get thrown off by this...



















As the question is long, feel free to only answer a few parts of it. However, don't hog all the easy parts like (c).
Where'd you get that question from?
 

leehuan

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Re: HSC 2016 3U Marathon

NEXT QUESTION:



I'll tone the difficulty back down after this one.
 
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