How many 2-letter "words" consist of two different letters arranged in alphabetical order? (Any two letters together is considered a "word." For example, one

Geez, you got to use algebra for this............CPhill can give you a good answer.

Note.....choosing an "a" first......we could pair this with 25 other letters in alphabetical order

Or...if we chose "b" first, we would have 24 other choices in alphabetical order

Or...choosing "c" first gives us 23 other choices in aplabetical order....so we have

25 + 24 + 23 + ....+  3 + 2 + 1   =     the sum of the first 25 positive integers =

(25)(26)/ 2  = 325 "words" in alphabetical order

We could also see this in another way.....we could take the permute of P(26,2)  = 650 different "words"  in any order....but ....only 1/2 of these would be any good, because the other half would not be in alphabtical order [the order would be reversed]  ....so   ....650 * 1/2  =  325

\(\begin{pmatrix} 26\\ 2 \end{pmatrix}\)

\(=\boxed{325}\)

\(\begin{pmatrix} 26\\ 2 \end{pmatrix}\)

\(=\boxed{325}\)