Discrete Math for Computer Science, unit: Combinatorics. Core concepts, terminology, and worked-example cues a college student meets for this unit, building on prior units without repeating them. Front: a term, concept, or short problem cue. Back: the definition, explanation, or answer.
16 cards · basic cards · AI-written, checked twice. Edit anything.
- What is combinatorics?
- The branch of mathematics studying counting, arrangement, and combination of objects
- What is the multiplication principle in counting?
- If one event can occur in m ways and another in n ways, both together occur in m times n ways
- What is the addition principle in counting?
- If two events cannot occur together, the total ways either occurs is the sum of their individual ways
- What is a permutation?
- An arrangement of objects where order matters
- What is a combination?
- A selection of objects where order does not matter
- What is the formula for permutations of n objects taken r at a time?
- n! divided by (n minus r)!
- What is the formula for combinations of n objects taken r at a time?
- n! divided by (r! times (n minus r)!)
- What does n! (n factorial) represent?
- The product of all positive integers from 1 up to n
- What is the pigeonhole principle?
- If more items are placed into fewer containers than items, at least one container holds more than one item
- What is a practical use of the pigeonhole principle?
- Proving that some collision or repetition must occur without identifying it explicitly
- What is the binomial theorem used for?
- Expanding expressions of the form (a plus b) raised to a power n
- What are binomial coefficients?
- The numeric coefficients in a binomial expansion, equal to combination values
- What is Pascal's Triangle?
- A triangular array of binomial coefficients where each number is the sum of the two above it
- What is a permutation with repetition?
- An arrangement where the same object can be selected more than once
- What is the difference between a permutation and a combination?
- A permutation considers order significant, while a combination does not
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