Combinations and their properties

Combinations $C_n^k$

A $k$ -element subset of $n$ distinct objects counts as one combination, no matter how you permute the chosen elements. $C_n^k=\dfrac{n!}{k!(n-k)!},\quad 0\leq k\leq n.$ Link to arrangements: $A_n^k=C_n^k\cdot k!$ — first choose the set, then order it in $k![/math]]** ways. **Symmetry:** **[[math]]C_n^k=C_n^{n-k}$ .

$C_n^0=C_n^n=1$ ; $C_n^1=n$

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