2021 WSMO Team Round/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, there are two capital letters we can choose. Now we split up the lowercase letters into two cases:

Case 1: the letter appears once. There are 6 of these.

Case 2: the letter appears twice. There are 3 of these. Notice that we can chose any letter afterwards, so .

Finally, the number of ways to pick a word is equal to . ~programmeruser