## Fun with Zeta !!!

Mr. and Mrs. Zeta wanted to name their baby Zeta so that its monogram (first, middle and last initials) will be in alphabetical order with no letters repeated. How many such monograms are possible?

*— Nalin Pithwa *

(Ref: Prof Titu Andreescu’s literature).

### Like this:

Like Loading...

*Related*

## 2 Comments

Since last name will start with Z, we just need to maintain an alphabetical order for initials of first and middle name. Since there are 26 alphabets in English language, for first name initial alphabet we have 25 choices. But since alphabets can’t repeat, for each choice of first name initial letter we have “25-(position of alphabet used for first name)” choices for initial letter of middle name (should be non-zero) . So, to count the total number of monograms possible, we make cases by fixing an alphabet for first name and counting available alphabets for middle name.

Total distinct monograms possible= 24+23+22+…+1 = 300

🙂