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.
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- What is combinatorics?
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The branch of mathematics studying counting, arrangement, and combination of objects- What is the multiplication principle in counting?
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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?
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If two events cannot occur together, the total ways either occurs is the sum of their individual ways- What is a permutation?
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An arrangement of objects where order matters- What is a combination?
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A selection of objects where order does not matter- What is the formula for permutations of n objects taken r at a time?
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n! divided by (n minus r)!- What is the formula for combinations of n objects taken r at a time?
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n! divided by (r! times (n minus r)!)- What does n! (n factorial) represent?
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The product of all positive integers from 1 up to n- What is the pigeonhole principle?
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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?
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Proving that some collision or repetition must occur without identifying it explicitly- What is the binomial theorem used for?
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Expanding expressions of the form (a plus b) raised to a power n- What are binomial coefficients?
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The numeric coefficients in a binomial expansion, equal to combination values- What is Pascal's Triangle?
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A triangular array of binomial coefficients where each number is the sum of the two above it- What is a permutation with repetition?
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An arrangement where the same object can be selected more than once- What is the difference between a permutation and a combination?
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A permutation considers order significant, while a combination does not
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