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# Proof of Binomial Distribution by Induction watch

1. the question ive been asked is..

Show C(n,r), defined by

C(n, r) = n! / r!(n-r)! , n ∈ N , r = 0,1... n

always lies in N using a proof by induction.

i need help, i have a rough idea about proof by induction but i dont no how to apply it to this question. can anybody help me?
2. You probably want to state that r<=n somewhere as well.

Then start by showing it holds for n=1 (=>r=1 or r=0 and r=0 is trivial/not very interesting)

Assume it holds for n. Then try finding a relationship between the n+1 case and n case.

Please post back your attempt and we can give more specific help.
3. ive sed n=1 and r=0...

1! / 0!(1-0)! which equals 1.

when i put it is terms of k: n=k and then n=k+1 i get confused on how to work it out. in k+1 do i make r=0 again, or do i move onto the next number, which is r=0? i am unsure oon the whole question to be honest lol
4. ive put in n=1 and r=0 to get 1. i also put in n=1, r=1 to get 1 also. i then wrote it in terms of k where n=k. then i put n=k+1. wen i put r=1 into the k+1, i get:

(k+1)! / k! which proves that it always lies in N.

is this correct because im not sure about it, nobody else in my group no's if it is correct either?
5. I would say the simplest thing is to work from the identity

(and use induction on n).
6. (Original post by DFranklin)
I would say the simplest thing is to work from the identity

(and use induction on n).
im not sure i understand... can u be abit more specific please? thanks
7. Well, if you're using induction on n, you know the two terms on the RHS are integers (by the induction hypothesis). So, what can we say about the LHS?
8. (Original post by DFranklin)
Well, if you're using induction on n, you know the two terms on the RHS are integers (by the induction hypothesis). So, what can we say about the LHS?
i really dont understand... y r the two terms intergers? wat can i say about the LHS?
9. Please don't use text speak, it is against the forum rules.

As far as the question goes - I think you'd be best speaking to your teacher/lecturer. It looks like you are very confused, and they need to know that.
10. (Original post by DFranklin)
Please don't use text speak, it is against the forum rules.

As far as the question goes - I think you'd be best speaking to your teacher/lecturer. It looks like you are very confused, and they need to know that.
its not that, its just my teacher never taught me that equation u shows me in the previous post.

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Updated: January 18, 2010
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