Counting Principles

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Last updated 10:14 PM on 5/9/26
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14 Terms

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Combination

When order doesn’t matter

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Combination equation

Same as binomial theorem - nCr = n!/r!(n-r)!

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Permutation

Order matters

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Permutation equation

nPr = n!/(n-r)!

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Distinct Permutations Equation

n!/(n1!*n2!*…nk!)

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Nothing can be repeated

n!

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Nothing can be repeated

n!

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or, if one task can be done in m ways and a second mutually exclusive task can be done in n ways

Add (m + n)

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And, one event can occur in m ways and another can occur in n ways

Multiply (mn)

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When making one choice doesn’t affect the rest (items can be reused)

n^k

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Yes/No, True/False

2^n

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Creating ordered list (with repetition allowed)

n^k (y^z)( a^b ) …

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Total number of options

n

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Selection Amount

r