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Counting Principles

Updated 01 Oct 2026

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What it is
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  rules for counting outcomes before assigning probabilities
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Formula
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  sequential choices: multiply the number of available choices at each stage
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  ordered selection without replacement: $P(n,r)=n!/(n-r)!$
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  unordered selection without replacement: $\binom nr=n!/[r!(n-r)!]$ .
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Example
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  assigning three distinct offices to different people from a group of $25$ gives $25\cdot24\cdot23=13800$ assignments.
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  Under uniform selection, one specified assignment has probability $1/13800$ .
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  With $15$ men and $10$ women, the probability of men in the first two offices and a woman in the third is $(15/25)(14/24)(10/23)=7/46$ .
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Linked references 1

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