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Multiplication Principle


The multiplication principle, also called the fundamental counting principle, states that if a procedure consists of k successive choices and the ith choice can be made in n_i ways for every combination of preceding choices, then the procedure can be performed in

 product_(i=1)^kn_i

ways. In particular, if one choice can be made in m ways and a second in n ways for each first choice, then the pair of choices can be made in mn ways. No probabilistic independence assumption is involved.


See also

Cartesian Product, Combinatorics, Enumeration Problem

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Cite this as:

Weisstein, Eric W. "Multiplication Principle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MultiplicationPrinciple.html

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