PERMUTARI
Reprezinta numarul tuturor submultimilor unei multimi. (P indice n este egal cu n factorial)
Formula permutari
$$P_{n} = n!$$
unde:
$P_{n}$ = permutari de n
n! = n factorial
$$n! = 1 \cdot 2 \cdot 3 \cdot ... \cdot n$$
Formula de recurenta a permutarilor
Permutari exercitii rezolvate
ARANJAMENTE
Reprezinta numarul tuturor submultimilor ordonate de k elemente ale unei multimi de n elemente.
Formula aranjamente
$$A_{n}^{k} = \frac{n!}{(n - k)!}$$
$$sau$$
$$A_{p}^{n} = n(n - 1) \cdot ... \cdot (n - p + 1) = \frac{n!}{(n - p)!}$$
Formula de recurenta a aranjamentelor
$$A_{n}^{p} = (n - p + 1) A_{n}^{p - 1}, ∀ \ p \ > \ 1$$
Aranjamente exercitii rezolvate
COMBINARI
Reprezinta numarul tuturor submultimilor (neordonate) de k elemente ale unei multimi de n elemente.
Formula combinari
$$C_{n}^{k} = \frac{n!}{k!(n - k)!}$$
$$sau$$
$$C_{n}^{p} = \frac{A_{n}^{p}}{P_{p}} = \frac{n!}{p!(n - p)!}, \ cu \ 0 \ ≤ \ p ≤ \ n,$$
$$C_{n}^{k} = \frac{n!}{k!(n - k)!}$$
Formula de recurenta a combinarilor
$$C_{n}^{p} = C_{n - 1}^{p} + C_{n - 1}^{p - 1}$$
Formula de recurenta a combinarilor demonstratie
