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$$\dbinom{n}{m}=\dfrac{n!}{m!(n-m)!}$$

$$\dbinom{n+m}{n}=\dbinom{n+m}{m}$$

$$\dbinom{n+r+1}{r}=\sum_{i=0}^{r}\dbinom{n+r}{r}$$

$$\dbinom{n}{l}\dbinom{l}{r}=\dbinom{n}{r}\dbinom{n-r}{l-r}$$

$$\sum_{i=0}^{n}\dbinom{n}{i}=2^n$$

$$\sum_{i=0}^{n}(-1)^i\dbinom{n}{i}=0$$

$$\sum_{i=r}^{n}\dbinom{i}{r}=\dbinom{n+1}{r+1}$$

$$(x+y)^n=\sum_{i=0}^{n}\dbinom{n}{i}x^iy^{n-i}$$

$$\sum_{i=0}^{n}\dbinom{n}{i}^2=\dbinom{2n}{n}$$

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