What means number on number?

Question

What does the following notation mean?

$$k \choose n$$

If you didn't understand me see my question and the first answer that was accepted Permutation and combinations using chairs?

Answer 1

$$\binom{n}{r}=nCr=\frac{n!}{r!(n-r)!}$$ $$\text{Where }x!=1\cdot2\cdot3\cdot\ldots\cdot x$$ E.g. $$\binom{7}{5}=\frac{7!}{5!\cdot2!}=\frac{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7}{(1\cdot2\cdot3\cdot4\cdot5)\cdot(1\cdot2)}=\frac{6\cdot7}{2}=21$$

Answer 2

Another way to read

$${n \choose r}$$

is "n choose r" -- it's the number of ways to choose a group of $r$ things out of $n$ things. The order of the things once you've chosen them doesn't matter.

Rhys' answer has the formula for this.