Unit 8: Counting rules & factorials

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Rule cards

Steps that build ONE outcome → multiply the number of choices: e₁ × e₂ × … × eₙ.

Traps

Added the choices.
10 jeans + 15 shirts + 4 shoes = 29
✓ 10 × 15 × 4 = 600; 4 styles × 4 stitches × 7 yarns = 112

Repeats allowed (digits, PINs) → n × n × … = nʳ. No repeats (people, cards, letters of a WORD) → n × (n − 1) × (n − 2) …

Traps

Counted down when repeats were allowed.
zip codes → 10·9·8·7·6
✓ repeats allowed → 10⁵ = 100,000
Used nʳ when items can't repeat.
no-repeat zip → 10⁵
✓ 10·9·8·7·6 = 30,240
Left 0 out of the digits.
9 choices per digit
✓ digits 0–9 = 10 choices

n! = n(n − 1)(n − 2)…1; arrange ALL n different things = n!; 0! = 1 and 1! = 1.

Traps

Said 0! = 0.
0! → 0
✓ 0! = 1
Stopped one factor early or started one too high.
6 games on a shelf → 5! = 120
✓ 6 games on a shelf = 6! = 720; 8 dogs = 40,320
Wrote nⁿ instead of n!.
6 games → 6⁶
✓ 6! = 720

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