## anonymous one year ago Simplfy (n) - (n-1) (r) (r)

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1. anonymous

$\left(\begin{matrix}n \\ r\end{matrix}\right) - \left(\begin{matrix}n-1 \\ r\end{matrix}\right)$

2. anonymous

simplify

3. welshfella

|dw:1443370171228:dw|

4. welshfella

I'm feeling my way here ... and i'm not sure if it will lead to much simplification...

5. welshfella

oh i misread the question the second part is |dw:1443371547831:dw|

6. anonymous

yea

7. welshfella

well i've got an expression which contains factorials but its not that simple!

8. welshfella

|dw:1443372120105:dw|

9. anonymous

\begin{align*}\binom nr-\binom{n-1}r&=\frac{n!}{r!(n-r)!}-\frac{(n-1)!}{r!(n-1-r)!}\\[1ex] &=\frac{(n-1)!}{r!(n-1-r)!}\left(\frac{n}{(n-r)}-1\right)\\[1ex] &=\frac{(n-1)!}{r!(n-1-r)!}\left(\frac{n-(n-r)}{(n-r)}\right)\\[1ex] &\vdots \end{align*}