Chitsanzo cha Mafunso Okambirana za Permutation
Kusinthasintha kwa zinthu ndi kukonzedwanso kwa zinthu m'dongosolo linalake. Mu masamu, lingaliro ili nthawi zambiri limagwiritsidwa ntchito kuwerengera njira zomwe gulu la zinthu lingakonzedwere. Pansipa, tikambirana zitsanzo zingapo za mavuto a kusintha kwa zinthu ndi mafotokozedwe awo athunthu.
Tanthauzo la Permutation
Kusinthasintha kwa seti ndi kusinthidwa kwa zinthu zake m'dongosolo linalake. Ngati pali zinthu \( n \) , kusinthaku kumawonetsedwa ndi \( P(n) \) kapena makamaka, \( P(n, r) \) pa \( r \) kusintha kwa zinthu \( n \) . Fomula yoyambira ya kusinthaku ndi iyi:
\[ P(n) = n! \]
kumene \( n! \) (n factorial) ndi chinthu chopangidwa ndi manambala onse abwino ochepera kapena ofanana ndi \( n \).
Pakadali pano, fomula yosinthira \( r \) ya zinthu \( n \) ndi iyi:
\[ P(n, r) = \frac{n!}{(nr)!} \]
Mafunso ndi Kukambirana Zitsanzo
Chitsanzo cha Funso 1
vuto:
Kodi mabuku 4 osiyanasiyana angakonzedwe m'njira zingati pa shelufu?
Kukambirana:
Kuti tikonze mabuku anayi osiyanasiyana, tingagwiritse ntchito njira yowerengera makonzedwe onse a mabuku:
\[ P(4) = 4! = 4 \nthawi 3 \nthawi 2 \nthawi 1 = 24 \]
Kotero, pali njira 24 zokonzera mabuku anayi osiyanasiyana pa shelufu.
Chitsanzo cha Funso 2
vuto:
Kodi pali njira zingati zomwe zingatheke zosankhira ndikukonza mamembala atatu a gulu la anthu asanu mu dongosolo loperekedwa?
Kukambirana:
Timagwiritsa ntchito njira yosinthira \( P(n, r) \) pomwe \( n = 5 \) ndi \( r = 3 \):
\[ P(5, 3) = \frac{5!}{(5-3)!} = \frac{5!}{2!} = \frac{5 \nthawi 4 \nthawi 3 \nthawi 2!}{2!} = 5 \nthawi 4 \nthawi 3 = 60 \]
Kotero, pali njira 60 zosankhira ndikukonza mamembala atatu a gulu la anthu 5 motsatira dongosolo linalake.
Chitsanzo cha Funso 3
vuto:
Kodi mawu oti “MASA” angakonzedwe m'njira zingati kuti zilembo zisabwerezedwenso?
Kukambirana:
Mawu akuti "MATH" ali ndi zilembo zinayi zosiyana. Tingagwiritse ntchito njira yowerengera makonzedwe onse a zilembo izi:
\[ P(4) = 4! = 4 \nthawi 3 \nthawi 2 \nthawi 1 = 24 \]
Kotero, pali njira 24 zokonzera zilembo mu liwu lakuti "MATH".
Chitsanzo cha Funso 4
vuto:
Kuchokera pa manambala 1, 2, 3, 4, 5, ndi manambala angati a manambala atatu omwe angapangidwe ngati palibe manambala obwerezedwa?
Kukambirana:
Kuti tipange nambala ya manambala atatu kuchokera ku manambala 5 osiyanasiyana pomwe palibe manambala omwe amabwerezedwa, timagwiritsa ntchito permutation \( P(5, 3) \):
\[ P(5, 3) = \frac{5!}{(5-3)!} = \frac{5!}{2!} = \frac{5 \nthawi 4 \nthawi 3 \nthawi 2!}{2!} = 5 \nthawi 4 \nthawi 3 = 60 \]
Kotero, pali njira 60 zopangira nambala ya manambala atatu kuchokera ku manambala 1, 2, 3, 4, ndi 5 popanda kubwereza manambala aliwonse.
Chitsanzo cha Funso 5
vuto:
Pali osewera 6, A, B, C, D, E, ndi F. Adzakonzedwa m'magulu atatu apamwamba pamasewerawa. Kodi osewera atatuwa angakonzedwe m'njira zingati?
Kukambirana:
Apa tikupemphedwa kuti tikonze osewera atatu motsatira dongosolo linalake mwa osewera onse 6. Fomula yomwe imagwiritsidwa ntchito ndi permutation \( P(n, r) \) pomwe \( n = 6 \) ndi \( r = 3 \):
\[ P(6, 3) = \frac{6!}{(6-3)!} = \frac{6!}{3!} = \frac{6 \nthawi 5 \nthawi 4 \nthawi 3!}{3!} = 6 \nthawi 5 \nthawi 4 = 120 \]
Kotero, pali njira 120 zokonzera osewera atatu mwa 6 motsatira dongosolo linalake.
Chitsanzo cha Funso 6
vuto:
Dziwani kuchuluka kwa mawu oti “YUNIVESITI” omwe ali ndi ma permutations angati kuti ma vowels azikhala pafupi nthawi zonse.
Kukambirana:
Mawu akuti “YUNIVESITI” ali ndi zilembo 11, ndipo mavawelo ndi U, I, E, I, A. Taganizirani gulu la mavaweloli ngati gawo limodzi.
Kotero, tili ndi: (UIEIA), N, V, R, S, T, ndi S (ngati gawo limodzi). Kenako tiyenera kukonza mayunitsi 7 awa:
\[ P(7) = 7! = 5040 \]
Komabe, mu gulu la mawu (UIEIA), akhoza kukonzedwa mu:
\[ P(5) = 5! = 120 \]
Kotero, kusintha konse kwa ma permutation ndi awa:
\[ 7! \nthawi 5! = 5040 \nthawi 120 = 604800 \]
Kotero, pali njira 604800 zopangira mawu akuti “YUNIVESITI” pomwe mavawelo onse nthawi zonse amakhala pafupi.
Mapeto
Kusinthasintha ndi dongosolo la zinthu kapena malo m'dongosolo linalake, ndipo lingaliro ili limagwiritsidwa ntchito m'magawo osiyanasiyana, kuphatikizapo masamu, sayansi ya makompyuta, ndi ziwerengero. Mwa kuzindikira ndikugwiritsa ntchito njira yoyenera, titha kuwerengera mosavuta kuchuluka kwa makonzedwe omwe angatheke.
Zitsanzo zomwe zaperekedwa zikuwonetsa momwe ma formula a permutation amagwirira ntchito komanso momwe angagwiritsidwire ntchito pazochitika zosiyanasiyana. Kumvetsetsa bwino ma permutation ndikofunikira kwambiri pothetsa mavuto ovuta ophatikizana ndipo ndikofunikira kwambiri popanga malingaliro othetsera mavuto.
