Problem:
Mr. and Mrs. Zeta want to name 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?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Any two-element subset of the first letters of the alphabet in alphabetical order together with will produce a suitable monogram; furthermore, all suitable monograms are of this form. The number of such two-element subsets is .
The last initial is fixed at . If is chosen for the first initial, there are choices for the second. If is chosen, there are choices, etc. Therefore (using ) the number of monograms is