Product Rule Outfits - Combinatorics and Search Step by Step

Count outfits by multiplying independent choices. This is a small deterministic example, not solver engineering.

Example

Count outfits by multiplying independent choices. When each shirt can be worn with each pair of pants, every shirt opens up the full set of pants, so the totals multiply rather than add. This is the fundamental counting principle: for independent choices made in sequence, multiply the number of options at each stage to get the number of combined outcomes.

highlighted = computed this step

Step 1 — Choices

Set up the exact small combinatorics values.

\begin{array}{c|c}\text{shirts, pants}&\text{(3, 2)}\end{array}

Step 2 — Multiply

Compute the highlighted combinatorics value.

\begin{array}{c|c}\text{shirts times pants}&\hlmath{\text{6}}\end{array}

combinatorics-search Every row is intentionally ordered and pinned to the lesson specification.