Using a graph analogy, this would be easier to understand.
Suppose, we have three colours , possible color combination pairs we can have is $\binom{n}{2}+n$,
Self Loops represent when both prints can be colored by the same color.
Three colours Red,Blue,Green. here $n=3$
Number of possible pairwise colorings which can be done is $\binom{3}{2}+3=6$
Now to color 26 alphabets, sufficient number of colors required. is $\min_{k} \binom{k}{2} \geq 26$.
Solving it we get $k=7$.
