I-Calculator ye-Permutation (nPr)

Bhala izilungiselelo ezilungisiwe zezinto r ezikhethiwe kusuka ku-n.

Izishintsho (nPr) —
Ifomula —

Iziphetho zivuselelwa uma ubhala.

Ingabe le calculator ikulethela impendulo efanele?

Malunga nale khadi

A permutation counts how many ways you can arrange r items chosen from a set of n, where order matters — so first, second and third place are three different outcomes. This calculator returns the exact count and the formula it used, even for large n and r.

The formula is nPr = n! / (n − r)!, which is the same as multiplying the top r numbers counting down from n. For 10 items taken 3 at a time, that is 10 × 9 × 8 = 720. Choosing none gives nP0 = 1, and arranging all of them gives nPn = n!. You cannot choose more items than you have, so if r is greater than n the tool returns a dash.

Permutations answer "how many ordered sequences?" — the number of possible race finishes, seating orders, PIN codes or ranked shortlists. When order does not matter, use a combination instead, which is always the smaller count.

Imibuzo ebuzwa kaningi

Yini ushintsho phakathi kwe-permutation ne-combination?

Kuhlelo lokushintshana, ukulandelana kubaluleke kakhulu (okuqala, owesibili, owesithathu yimiphumela ehlukene); kuhlanganise, akunjalo. Kuhlala kunezishintsho eziningi njengokuba kuhlanganise.

Yini ifomu lokushintshana?

nPr = n! / (n − r)!. Izingxenye ezingu-10 zithathwa njenge-3 ngasikhathi sinye: 10 × 9 × 8 = 720.

Ngabe kufanele ngisebenzise i-permutation?

Uma ukulandelana kubaluleke kakhulu: ukudweba abaqedela, ukugcwalisa indawo yokuqala/yesibili/yesibili, ukuphumula abantu emgqeni, noma ukwakha ikhodi elungisiwe.

Yini ezoba uma r ikhulu kuna-n?

Awukwazi ukuhlela izinto eziningi kunalokho okwenzekile, ngakho-ke imiphumela ayicacisiwe futhi ithuluzi libuyisela umgwaqo.

Yini i-nP0?

Kuyi-1 — kunendlela eyodwa kuphela yokuhlela okuthile, ukuhlela okungenalutho.

Yini i-nPn?

Ilingana ne n!, ngoba ukuhlela zonke izimo n ngokulandelana kuyinto efanayo ne factorial egcwele. Umzekelo 4P4 = 4! = 24.

Ama-calculators ahlobene

I-Calculator yokuxhuma (nCr) I-Calculator ye-Factorial

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API — sebenzisa le calculator kusuka kukhodi

Nquma le calculator njenge JSON evulekile yendawo yokuqeda - akukho isithonjana esidingekayo. Thumela amaxabiso endawo ngezansi njengezilungiselelo zombuzo noma i-JSON. Noma yini ongayishiya isebenzisa iphutha elifanayo elifakwe ngaphambili lekhasi; ipharamitha engaziwa yi-400, ayikho i-zero emnyama. Funda i-API egcwele →

Ingxenye yendawo

GET https://calculator.free/api/v1/permutation/

curl

curl "https://calculator.free/api/v1/permutation/?n=10&r=3"

JavaScript fetch()

const r = await fetch(
  "https://calculator.free/api/v1/permutation/?" + new URLSearchParams({
    "n": "10",
    "r": "3"
  }));
const data = await r.json();
console.log(data.results);

Izibalo ziyisilinganiso esisetshenziswa ukuqondisa kuphela, hhayi ukucebisa ngezimali, ukwelashwa noma ukukhokha.