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Proving ${{n} \choose {r}}={{n-1} \choose {r-1}}+{{n-1} \choose r}$ when $1\leq r\leq n$

I have a dilemma here, how can we show Pascal's Rule :

Show that $$ \binom{n}{r} = \binom{n-1}{r-1} + \binom{n-1}{r}, 1 \leq r \leq n. $$

I tried solving the right side by substituting everything into the combination's formula but everything gets complicated.. thanks

PS: I tried substituting real valued numbers, and it works, but it should be proof by means of mathematical manipulation.

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    tnx. kannapan sampth2012-01-22

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