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Galdr Spell · Kap 3

Drainage

A pool of N. Draw S. The pool shrinks with every pick. Count the ways.

The pool shrinks. Every pick removes one from the pool. The next pick has fewer to choose from. The product of the shrinking choices is the count.
See the Web

The Branching

Pick a formula in Step 1 to see how the pool fans out.

N = 10, S = 3
Walk the spell

Step 1 — Two Questions

Answer two questions. They determine the formula.

Does order matter?
Yes — ordnet
Positions, ranks. 1st ≠ 2nd.
No — uordnet
Just a group. Who, not what order.
Does the pool refill?
Yes — med tilbakelegging
Item goes back. Same pool every round.
No — uten tilbakelegging
Each pick removes one. Pool shrinks.
Pool refillsPool drains
Order mattersNSnPr
Order doesn’t matter(ikke pensum)nCr
When Drainage Feeds the Probability House

When the problem asks for a probability:

Mulige — total ways (denominator).

Gunstige — ways that satisfy the condition (numerator).

P = gunstige / mulige

Drainage counts. Laplace converts to mass. The Probability House composes.

Formula Reference — Kap 3
n!Full drainage
n! = n × (n−1) × … × 1
Every item leaves the pool. nPr and nCr are built from n!.
nPr — PermutationsOrdered
nPr = N! / (N−S)! = N × (N−1) × … × (N−S+1)
S items leave. Order matters. The (N−S)! cancels the unused rounds.
nCr — CombinationsUnordered
nCr = N! / (S!(N−S)!) = nPr / S!
Same drainage as nPr, then ÷ S! to strip the costume-count.
NSNo drainage
NS = N × N × … (S times)
Pool refills. Every round has the same N choices.