36-10 Mr. and Mrs. Zeta want to name baby Zeta so that the first letters of the baby's first, middle, and last names are in alphabetical order and the letters are distinct. The number of possible names is
(A) 276.
(B) 300.
(C) 552.
(D) 600.
(E) 15600.
(40th American High School Mathematics Examination, 1989)
[Solution] If little Zeta's last name is Zeta, then the first letter of their given name, the baptismal name, can be
$A, B ; A, C ; A, D ; \cdots \quad ; A, Y$; (second letter $B \rightarrow Y$ )
$B, C ; \quad B, D ; \quad B, E ; \quad \cdots \quad ; \quad B, Y ; \quad$ (second letter $C \rightarrow Y$ ) .....
$W, X ; W, Y$;
(second letter $X \rightarrow Y$ )
$X, Y$.
There are $24+23+22+\cdots+2+1=\frac{24 \cdot 25}{2}=300$ possibilities. Therefore, the answer is $(B)$.