Question

How many combinations exist of the letters w, x, y, z, taking two at a time?

Answer 1

The binomial coefficient

$\displaystyle \binom{4}{2} = \dfrac{4!}{2!(4-2)!} = \dfrac{4\cdot 3}{2} = 2\cdot 3 = 6$

Tells you that there are 6 ways of choosing a subset of two letters from the four given letters.

For each of these subsets there are two combinations (you can interchange the two letters: say that you choose the subset wz, you have the two combinations wz and zw)

So, there is a total of 12 combinations of the letters w, x, y, z, taking two at a time.