Combination (Probability)

Notation §

def. Number of Choosing $k$ from $n$ items:

$$\left(\genfrac{}{}{0ex}{}{n}{x}\right)=\{\begin{array}{ll}\frac{n!}{(n-k)!\cdot k!}& n\ge x\\ 0& \text{else}\end{array}$$

NOTATION. $N\cdot (N-1)\cdot (N-2)\cdots (N-k)=N_{k-1}$