Question

I flat out do not understand what the binomial coefficient thing means. I know it relates to pascal's triangle, but I don't literally understand what it means.

Answer 1

\[\left(\begin{matrix}a \\ k\end{matrix}\right)\] So what does the spot of a and k represent?

Answer 2

a is total , k is the time repeated!

Answer 3

\[\left(\begin{matrix}p \\ k\end{matrix}\right) =\left\{ \frac{ p(p-1)(p-2)...(p-k+1) }{ p! } \right\}\]

So in this case k represents the total number of terms you're multiplying out. Specifically if I said k=3 it would be:

\[\left(\begin{matrix}p \\3\end{matrix}\right)=\left\{ \frac{ p(p-1)(p-2) }{ p! } \right\}\] apparently? I guess I don't understand why or where this is coming from, it just seems random.

Answer 4

I need context I guess. Why wouldn't it be p(p+1)(p+2)/p! for instance?

Answer 5

By the factorial definition, you count down from max value n. For example, n = 5
5! = 5 * 4 * 3 * 2 *1 = 120

Answer 6

What does that have to do with this?

Answer 7

I know what factorials are, 1!=1, 2!=2, 3!=6, 4!=24, etc... but I didn't know they mattered in that 3!=3*2*1 not 1*2*3 which is interesting I suppose but not sure I know the overarching theme of this stuff...

Answer 8

Don't you recognize: 5 * ( 5 -1) * ( 5 -2) ...

Answer 9

I see. but I guess I still don't see the point though... What's it all for?

Answer 10

It explains the combination a C k formula, you post above, and wonder why it isn't:
p ( p+1) (p+2) ...

Answer 11

So what's a Ck formula is my next question.

Answer 12

It's been a while since I last took a math class and need to understand this notation. If you're saying I need to understand Ck formula, what the hell is it so I can try to find out what I need to know. It's a sequence or series I believe but beyond that I'm not sure.