Cokovata

Ena fika, na cokovata e dua na digidigi ni veika mai na dua na seti ka tiko kina na lewenilotu duidui, me vaka na ituvatuva ni digidigi e sega ni bibi (sega ni vaka na veisau).Me kena ivakaraitaki, soli e tolu na vuanikau, kaya e dua na yapolo, e dua na moli kei dua na pea, e tolu na isoqoni ni rua e rawa ni dregati mai na seti oqo: e dua na yapolo kei dua na pea; e dua na apolo kei dua na moli; se dua na pea kei dua na moli. E vakamatanitu cake, e dua na k-cokovata ni na seti S e dua na ilawalawa lailai ni k duidui na veika e S. O koya gona, e rua na isoqoni e cokovata kevaka ka kevaka walega na isoqoni yadua e tiko kina na lewenilotu vata ga. (Na ituvatuva ni lewenilotu ena seti yadua e sega ni bibi.) Kevaka e tiko ena seti n veika, na naba ni k-cokovata, vakatakilakilataki ena $C(n,k)$ se $C_{k}^{n}$ , e tautauvata kei na ivakarau ni binomial.

${\binom {n}{k}}={\frac {n(n-1)\dotsb (n-k+1)}{k(k-1)\dotsb 1}},$

ka rawa ni volai ena kena vakayagataki na vakaveika me vaka na $\textstyle {\frac {n!}{k!(n-k)!}}$ ena gauna cava ga $k\leq n$ , kei na kena e saiga gauna cava $k>n$ . Na fomula oqo e rawa ni rawati mai na kena dina ni yadua k-cokovata ni dua seti S ni n lewenilotu sa $k!$ veisautaki vakakina $P_{k}^{n}=C_{k}^{n}\times k!$ or $C_{k}^{n}=P_{k}^{n}/k!$ .^[1] Na seti ni kece k-cokovata ni dua seti S e dau vakatakilakilataki ena $\textstyle {\binom {S}{k}}$ .

Na kena cokovata e dua na digidigi ni n veika e tauri k ena dua na gauna ka sega ni tokaruataki. Me dusia na cokovata e vakatarai kina na tokaruataki, na vosa k-cokovata vata tokaruataki, k-veimataqali,^[2] se k-digidigi,^[3] era dau vakayagataki.^[4] Kevaka, ena ivakaraitaki e cake, e rawa ni rua na dua na mataqali vuanikau ena tiko kina e 3 tale na 2-digidigi: dua e rua na yapolo, dua e rua na moli, kei dua e rua na pea.

Dina ga ni lailai na seti ni tolu na vuanikau me volai kina e dua na lisi taucoko ni veivakaduavatataki, oqo e yaco me sega ni rawa ni vakayacori ni sa tubu na levu ni seti. Me kena ivakaraitaki, e dua na liga poker e rawa ni vakamacalataki me vaka e dua na 5-cokovata (k = 5) ni kadi mai na dua 52 kadi deki (n = 52). Na 5 kadi ni liga era duidui kece, kei na ituvatuva ni kadi ena liga e sega ni bibi. E 2,598,960 na cokovata vakaoqo, kei na madigi ni droini ni dua na liga ena vakaveitalia e 1 / 2,598,960.

Veitikina

↑ Reichl, Linda E. (2016). "2.2. Counting Microscopic States". A Modern Course in Statistical Physics. WILEY-VCH. p. 30. ISBN 978-3-527-69048-0.
↑ Mazur 2010, p. 10
↑ Ryser 1963, p. 7 also referred to as an unordered selection.
↑ When the term combination is used to refer to either situation (as in (Brualdi 2010)) care must be taken to clarify whether sets or multisets are being discussed.

[1] Reichl, Linda E. (2016). "2.2. Counting Microscopic States". A Modern Course in Statistical Physics. WILEY-VCH. p. 30. ISBN 978-3-527-69048-0.

[2] Mazur 2010, p. 10

[3] Ryser 1963, p. 7 also referred to as an unordered selection.

[4] When the term combination is used to refer to either situation (as in (Brualdi 2010)) care must be taken to clarify whether sets or multisets are being discussed.

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