bump. Looking for a couple more students.
School's coming up, so here's your chance to brush up and clarify and doubts before jumping into new material.
Khan academy has a lot of resources that could be helpful though it isn't catered for the HSC course. They're pretty amazing!
http://www.youtube.com/user/khanacademy?blend=1&ob=4#g/u
I had her for a teacher in Years 11 and 12 for Physics and I must say she wasn't a very good teacher. She relied too heavily on HSC Dotpoint, turned up late in half the lessons and made us do trivial activities like group presentations/ posters and power points.
In terms of tutoring, she could...
You just used part i, substitute k = n.
Expand each of the combinations like so:
nC0 + \frac{nC1}{n} + \frac{nC2}{n^{2}} +...\\=1 + \frac{n!}{(n-1)!1!n} + \frac{n!}{(n-2)!2!n^{2}} + ... \\ = 1 + \frac{1}{1!} + \frac{n(n-1)}{2!n^{2}} + ...
Then take the limit of the whole thing, and all the...
For the first one, I think you just calculate probabilities of all X's and compare them to find the biggest ie. X = 1.
P(X=1) = 0.25
P(X=2) = 3/14
P(X=3) = 5/28
P(X=4) = 1/7
P(X=5) = 3/28
P(X=6) = 1/14
P(X=7) = 1/28
For part 2, just add up X = 5,6,7 to get your answer.
[Edit: I'll double check...
In all solutions, you always have 5 Easts and 4 Norths, so if we represent the person's path as:
EEEEENNNN
it's just a matter of finding how many ways you can arrange them. 9!/4!5!
Ahh I think I can see where the ambiguity arises.
"carlo randomly chooses four tiles, how many distinct ways can he arrange them?"
It sounds like the choosing has already happened, so all you are doing is calculating how many ways he can arrange the four tiles that he has.
so 4*3*2*1...