2021 WSMO Team Round Problems/Problem 1

Problem

How many ways are there to pick a three-letter word using only letters from "Winter Solstice" such that the word is a capital letter followed by two lowercase letters? (A word does not have to be an English word, and the word can only use a letter in "Winter Solstice" as many times as it appears)

Proposed by sanaops9

Solution

First, the capital letter must be either "W" or "S", giving 2 choices. After removing the capital, we’re left with 12 lowercase letters from "interolstice", among which 3 letters ( "i", "t", and "e") appear twice, and the rest appear once. This gives 9 unique lowercase letters. We can form ordered pairs of distinct lowercase letters, and 3 more using the repeated letters ("ii", "tt", "ee"). So each capital letter leads to valid words, and the final answer is . ~pinkpig