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The multiplication principle

If one choice can be made in n ways and another in m ways, the two can be made together in n times m ways. The principle is the basis of all counting, from password combinations to the number of possible design variants.

N = n_1\cdot n_2\cdots n_k

number of combinations of k independent choices

N = n^k

k choices with n options each

Symbols

$n_i$	number of options in choice i
$k$	number of choices

Example

A 4-digit PIN:

$10^4 = 10\,000$ possibilities.

Check whether the choices are independent. If one choice limits another, count more carefully.

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Part of Discrete Mathematics: Combinatorics.