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permutations #

Shows k-permutations as filling ordered slots from a pool without replacement. The animation steps through each slot to emphasize order sensitivity, then highlights the falling product n·(n−1)·…·(n−k+1) and its equivalence to n!/(n−k)!; includes a special case where k=n to show full permutations equal n!.

canvasclick to interact

⏮◀◀▶▶STEP0.25x1xZOOM

t=0s

practical uses #

• 01.Counting possible PIN/password orderings (without repeating characters)
• 02.Enumerating task/job execution orders in scheduling problems
• 03.Counting arrangements in sampling without replacement (e.g., ordered draws from a deck)

technical notes #

Time-based staged animation: each slot fill is a phase, followed by a formula-equivalence fade-in. Uses grid snapping for a blocky aesthetic, responsive scaling via scale=min(w,h)/baseSize, and simple deterministic selection to illustrate "no replacement".

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