Binomial coefficient/Number of subsets/Remark

For the binomial coefficient

${\binom {n}{k}}$

there is an important interpretation. It describes the number of subsets with exactly ${}k$ elements inside a set with ${}n$ elements. For example, within a set with ${}49$ elements there are exactly

${}{\binom {49}{6}}={\frac {49\cdot 48\cdot 47\cdot 46\cdot 45\cdot 44}{6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}}=13983816\,$

subsets with ${}6$ elements. The inverse of this number is the probability to get at the lotto all six numbers right.