Muenzaniso weMibvunzo yeKukurukurirana kwePermutation
Kuchinja-chinja zvinoreva kurongwa kweseti kana zvinhu nenzira yakatarwa. Mumasvomhu, pfungwa iyi inowanzo shandiswa kuverenga kuti boka rezvinhu rinogona kurongwa sei. Pazasi, tichakurukura mienzaniso yakati wandei yematambudziko ekuchinjika pamwe netsananguro dzawo dzakakwana.
Tsanangudzo yePermutation
Kugadziriswa kweseti kurongwazve kwezvinhu zvayo nenzira yakatarwa. Kana paine zvinhu \( n \) , kugadziriswa kunoratidzwa ne \( P(n) \) kana kuti, \( P(n, r) \) ye \( r \) kugadziriswa kwezvinhu \( n \) . Fomura yekutanga yekugadziriswa ndeye:
\[ P(n) = n! \]
apo \( n! \) (n factorial) chiri chigadzirwa chenhamba dzese dzakanaka dziri pasi kana kuti dzakaenzana na \( n \).
Zvichakadaro, fomura yekubvumidza \( r \) yezvinhu \( n \) ndeiyi:
\[ P(n, r) = \frac{n!}{(nr)!} \]
Mibvunzo yemuenzaniso nekukurukurirana
Muenzaniso Mubvunzo 1
Problem:
Mabhuku mana akasiyana angarongwa sei pasherufu?
Kukurukurirana:
Kuti tironge mabhuku mana akasiyana, tinogona kushandisa fomura ye permutation kuverenga marongero ese anogoneka emabhuku:
\[ P(4) = 4! = 4 \kawa 3 \kawa 2 \kawa 1 = 24 \]
Saka, kune nzira makumi maviri neina dzekuronga mabhuku mana akasiyana pasherufu.
Muenzaniso Mubvunzo 2
Problem:
Pane nzira ngani dzekusarudza nekuronga nhengo nhatu dzechikwata chine nhengo shanu nenzira yakatarwa?
Kukurukurirana:
Tinoshandisa fomura yekubvumidza \( P(n, r) \) apo \( n = 5 \) uye \( r = 3 \):
\[ P(5, 3) = \frac{5!}{(5-3)!} = \frac{5!}{2!} = \frac{5 \kawa 4 \kawa 3 \kawa 2!}{2!} = 5 \kawa 4 \kawa 3 = 60 \]
Saka, kune nzira makumi matanhatu dzekusarudza nekuronga nhengo nhatu dzechikwata chine nhengo shanu nenzira yakati.
Muenzaniso Mubvunzo 3
Problem:
Izwi rekuti "MATH" ringarongwa nenzira dzipi kuti mabhii asadzokororwe?
Kukurukurirana:
Izwi rekuti "MATH" rine mabhii mana akasiyana. Tinogona kushandisa fomura ye permutation kuverenga marongerwo ese angangodaro emavara aya:
\[ P(4) = 4! = 4 \kawa 3 \kawa 2 \kawa 1 = 24 \]
Saka, kune nzira makumi maviri neina dzekuronga mavara mushoko rekuti "MATH".
Muenzaniso Mubvunzo 4
Problem:
Kubva panhamba 1, 2, 3, 4, 5, ingani nhamba dzine manhamba matatu dzinogona kuumbwa kana pasina manhamba anodzokororwa?
Kukurukurirana:
Kuti tigadzire nhamba ine manhamba matatu kubva panhamba 5 dzakasiyana pasina nhamba inodzokororwa, tinoshandisa permutation \( P(5, 3) \):
\[ P(5, 3) = \frac{5!}{(5-3)!} = \frac{5!}{2!} = \frac{5 \kawa 4 \kawa 3 \kawa 2!}{2!} = 5 \kawa 4 \kawa 3 = 60 \]
Saka, kune nzira makumi matanhatu dzekugadzira nhamba ine manhamba matatu kubva panhamba 1, 2, 3, 4, uye 5 pasina kudzokorora chero nhamba.
Muenzaniso Mubvunzo 5
Problem:
Kune vatambi vatanhatu, A, B, C, D, E, na F. Vacharongwa vari vatatu vepamusoro pamutambo. Vatambi vatatu ava vangarongwa nenzira dzipi?
Kukurukurirana:
Pano tinokumbirwa kuronga vatambi vatatu nenzira yakatarwa kubva pavatambi vatanhatu. Fomura inoshandiswa ndiyo permutation \( P(n, r) \) apo \( n = 6 \) uye \( r = 3 \):
\[ P(6, 3) = \frac{6!}{(6-3)!} = \frac{6!}{3!} = \frac{6 \kawa 5 \kawa 4 \kawa 3!}{3!} = 6 \kawa 5 \kawa 4 = 120 \]
Saka, kune nzira zana nemakumi maviri dzekuronga vatambi vatatu pavatanhatu nenzira yakatarwa.
Muenzaniso Mubvunzo 6
Problem:
Sarudza kuti izwi rekuti "UNIVERSITY" rine ma permutation mangani kuitira kuti mavhawero agare ari pedyo nepamwe chete.
Kukurukurirana:
Izwi rekuti "UNIVERSITY" rine mabhii gumi nerimwe, uye mavhawero acho ndiU, I, E, I, A. Funga nezveboka iri remavhawero sechikamu chimwe chete.
Saka, tine: (UIEIA), N, V, R, S, T, naS (inoonekwa seyuniti imwe chete). Zvadaro tinofanira kuronga aya mayuniti manomwe:
\[ P(7) = 7! = 5040 \]
Zvisinei, muboka revaimbi (UIEIA), vanogona kurongwa mu:
\[ P(5) = 5! = 120 \]
Saka, ma permutations ese ndeaya:
\[ 7! \kanguva 5! = 5040 \kanguva 120 = 604800 \]
Saka, kune nzira dzinosvika 604800 dzekugadzira izwi rekuti "UNIVERSITY" apo mavhawero ese anogara ari pedyo nerimwe.
Mhedziso
Kugadziriswa kwechinhu kana kuti seti nenzira yakatarwa, uye pfungwa iyi ine mashandisirwo akawanda muzvikamu zvakasiyana-siyana, kusanganisira masvomhu, sainzi yemakombiyuta, uye nhamba. Nekuziva nekushandisa fomura yakakodzera, tinogona kuverenga nyore nyore huwandu hwemagadzirirwo anogona kuitwa.
Mienzaniso yakapihwa inoratidza mashandiro anoita maformula epermutation uye kuti anogona kushandiswa sei mumamiriro akasiyana-siyana. Kunzwisisa kwakakwana mapermutation kwakakosha pakugadzirisa matambudziko akaomarara ekubatanidza uye kunokosha mukugadzira pfungwa dzekugadzirisa matambudziko.
