▓▒░RASTKO'S DIGITAL REALM░▒▓

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Permutations

September, 2026

Defintion

Permutation $P (S)$ is a particular ordering of set's elements:

ab c, a c b, ba c, b c a, c ab, c ba

We find the $∣ P (S)∣$ by using the rule of product.

Formulas

For a set of $k$ elements

k! = k \cdot (k - 1) \cdot (k - 2) \dots 3 \cdot 2 \cdot 1

For a set of $n$ elements, number of $k$ -element permutations

∣ P_{k}^{n} (S)∣ = \frac{n !}{( n - k )!} When k = n ∣ P_{n}^{n} (S)∣ = \frac{n !}{( n - n )!} ∣ P_{n}^{n} (S)∣ = \frac{n !}{1} ∣ P_{n}^{n} (S)∣ = n!

NOTES

See how this differs from Combinations