combinations #

Visualizes choosing k distinct items from n when order does not matter. The animation first builds an ordered pick (a k-permutation), then rapidly cycles through the k! different orderings of the same chosen items and collapses them into a single unordered subset token, reinforcing that combinations are permutations with order factored out. The bottom panel ties this to the formulas C(n,k)=n!/(k!(n-k)!) and C(n,k)=P(n,k)/k! with a numeric example (n=5,k=3).

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

01.Counting possible teams/committees chosen from a group (order irrelevant)
02.Computing probabilities in card/dice problems using binomial coefficients
03.Feature subset selection and search-space sizing in algorithms/ML (choose k items from n)

technical notes #

Pure Canvas2D, retro blocky rendering via grid snapping. Time-based 4.2s cycle split into 3 eased segments (pick ordered -> forget order -> show formula/count). Includes a tiny 3x5 pixel font for consistent green-on-black labeling without external fonts.

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