Kalkaaliyeyaasha Permutation (nPr)
Tixraac hababka loo qorsheeyay ee r waxyaabaha la doortay ka n.
Natiijooyinka cusbooneysiinta sida aad ku qorto.
Ku saabsan Kalkaaliyahan
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.
Su'aalaha badanaa la isweydiiyo
Waa maxay farqiga u dhexeeya permutation iyo isku darka?
In a permutation order arrimaha (ugu horeysay, labaad, saddexaad waa natiijooyinka kala duwan); in isku darka ma aha. Waxaa jira mar walba ugu yaraan sida badan permutations sida isku darka.
Waa maxay foomka permutation?
nPr = n! / (n − r)!. 10 waxyaabaha la qaaday 3 mar kasta: 10 × 9 × 8 = 720.
Goorma ayaan isticmaali karaa permutation?
Marka amarku yahay: ranging finishers, buuxinta koowaad / labaad / saddexaad meelaha, fadhiista dadka in line, ama dhismaha code la amray.
Maxaa dhacaya haddii r ka weyn yahay n?
Waxaad u diri kartaa waxyaabo badan oo aad leedahay, sidaas daraaddeed natiijada waa aan la qeexin oo qalabku wuxuu ku celinayaa dhagxaan.
Waa maxay nP0?
Waa 1 — waxaa jira si dhab ah hab mid ah in ay isku dayaan waxba, isku dayaya in ay ka baxaan.
Maxaa nPn?
Waa isku mid n!, sababtoo ah qaabeynta dhammaan n waxyaabaha si waafaqsan waa la mid ah sida factorial buuxa. tusaale ahaan 4P4 = 4! = 24.
API — isticmaal xisaabinta ka code
Wici xisaabinta sida free JSON endpoint - key ma loo baahan yahay. Dib u soo dir qiimaha goobta hoos ku qoran sida parameters su'aal ama JSON. Wax kasta oo aad ka maqan tahay isticmaalaa default la mid ah ee boggani waa hore loo buuxiyey la; parameter aan la aqoon waa 400, marnaba ma aha zero maqan. Akhri dhammaan API xuquuqda →
Xarafka
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);Natiijooyinka waa tirakoobka loogu talagalay tilmaamaha guud oo keliya, maaha dhaqaale, caafimaad ama talo bixin canshuur.