Counting & combinatorics

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   A signal is formed by arranging $9$ flags in a row, using $3$ identical red flags, $3$ identical blue flags, and $3$ identical green flags (flags of the same color cannot be told apart). How many distinguishable signal sequences can be formed using all the flags?

2. Warm-up

   A signal is formed by arranging $11$ flags in a row, using $5$ identical red flags, $2$ identical blue flags, and $4$ identical green flags (flags of the same color cannot be told apart). How many distinguishable signal sequences can be formed using all the flags?

3. Warm-up

   A signal is formed by arranging $10$ flags in a row, using $2$ identical red flags, $5$ identical blue flags, and $3$ identical green flags (flags of the same color cannot be told apart). How many distinguishable signal sequences can be formed using all the flags?

Problems shown under their original terms: Generated (template, solver-computed).