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13 cards from this deck
Small sample spaces - to visualise and verify possibilities
Multiply the number of choices at each step
Arrangements (permutations) of nnn distinct objects
n!=n×(n−1)×⋯×1n! = n \times (n-1) \times \dots \times 1n!=n×(n−1)×⋯×1
Arrangements where order matters
P(n,r)=n!(n−r)!P(n,r) = \frac{n!}{(n-r)!}P(n,r)=(n−r)!n!
Selections where order does not matter
C(n,r)=n!r!(n−r)!C(n,r) = \frac{n!}{r!(n-r)!}C(n,r)=r!(n−r)!n!
Solving problems with multiple overlapping groups
3×4=123 \times 4 = 123×4=12 combinations
4!=244! = 244!=24
5×3×2=305 \times 3 \times 2 = 305×3×2=30 outfits
120120120 ways
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