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Factorial
- The product of all positive integers to some number
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Permutations
- An ordered arrangement of a set or items
- Used when order matters and elements are not-reused (unless specified)
Complete Permutation
- , where is the number of items
- Used when arranging all items in a set
- “How many ways can the letters in ‘Lizard’ be rearranged?”
- “Lizard” → 6 characters;
Permutation with Replacement
- , where is the number of items in the set and is the number of items selected
- 10 possible digits, 4 slots → 10,000 possible pin codes.
- Choosing items where order matters and repetitions are allowed
Permutation without Replacement
- Choose a subset of items where the order matters and elements cannot be duplicated
Permutation with Constraints
- “How many ways can you arrange the letters ‘abcdefg’ where ‘bcd’ must stay together”
Combinations
- Choosing items from a set of items where order does not matter
Combination without Replacements
- “How many 5-card hands in a 52-card deck?”
Combination with Replacements
- “Roll 3 5-sided dice, order is irrelevant”
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