I. PERM\u00dcTASYON A. SAYMANIN TEMEL KURALI
\n1) Ayr\u0131k iki i\u015flemden biri m yolla, di\u011feri n yolla yap\u0131labiliyorsa, bu i\u015flemlerden biri veya di\u011feri m + n yolla yap\u0131labilir.
\n2) \u0130ki i\u015flemden birincisi m yolla yap\u0131labiliyorsa ve ilk i\u015flem bu m yoldan birisiyle yap\u0131ld\u0131ktan sonra ikinci i\u015flem n yolla yap\u0131labiliyorsa bu iki i\u015flem birlikte m . n yolla yap\u0131labilir. <\/p>\n
B. FAKT\u00d6R\u0130YEL
\n 1den n ye kadar olan sayma say\u0131lar\u0131n\u0131n \u00e7arp\u0131m\u0131na n fakt\u00f6riyel denir ve n! bi\u00e7iminde g\u00f6sterilir.
\n 0! = 1 olarak tan\u0131mlan\u0131r.
\n 1! = 1
\n 2! = 1 . 2
\n ……………..
\n ……………..
\n ……………..
\n n! = 1 . 2 . 3 . … . (n \u2013 1) . n
\n\u00dc n! = n . (n \u2013 1)!
\n\u00dc (n \u2013 1)! = (n \u2013 1) . (n \u2013 2)! dir.<\/p>\n
C. TANIM
\n r ve n sayma say\u0131s\u0131 ve r \u00a3 n olmak \u00fczere, n elemanl\u0131 bir k\u00fcmenin r elemanl\u0131 s\u0131ral\u0131 r lilerine bu k\u00fcmenin r li perm\u00fctasyonlar\u0131 denir.
\n n elemanl\u0131 k\u00fcmenin r li perm\u00fctasyonlar\u0131n\u0131n say\u0131s\u0131,<\/p>\n
\u00dc 1) P(n, n) = n!
\n2) P(n, 1) = n
\n3) P(n, n \u2013 1) = n! dir.<\/p>\n
D. TEKRARLI PERM\u00dcTASYON
\n n tane nesnenin; n1 tanesi 1. \u00e7e\u015fitten, n2 tanesi 2. \u00e7e\u015fitten, … , nr tanesi de r yinci \u00e7e\u015fitten olsun.<\/p>\n
n = n1 + n2 + n3 + … + nr
\nolmak \u00fczere, bu n tane nesnenin n li perm\u00fctasyonlar\u0131n\u0131n say\u0131s\u0131,<\/p>\n
E. DA\u0130RESEL (D\u00d6NEL) PERM\u00dcTASYON
\n n tane farkl\u0131 eleman\u0131n d\u00f6nel (dairesel) s\u0131ralanmas\u0131na, n eleman\u0131n dairesel s\u0131ralamas\u0131 denir.
\n n eleman\u0131n dairesel s\u0131ralamalar\u0131n\u0131n say\u0131s\u0131 :<\/p>\n
(n \u2013 1)! dir.<\/p>\n
n tane farkl\u0131 anahtar\u0131n yuvarlak (halka bi\u00e7imindeki) bir anahtarl\u0131\u011fa s\u0131ralanmalar\u0131n\u0131n say\u0131s\u0131 :<\/p>\n
II. KOMB\u0130NASYON
\nTANIM
\n r ve n birer do\u011fal say\u0131 ve r \u00a3 n olmak \u00fczere, n elemanl\u0131 bir A k\u00fcmesinin r elemanl\u0131 alt k\u00fcmelerinin her birine, A k\u00fcmesinin r li kombinasyonu (gruplamas\u0131) denir.
\n n eleman\u0131n r li kombinasyonlar\u0131n\u0131n say\u0131s\u0131<\/p>\n
Perm\u00fctasyonda s\u0131ralama, kombinasyonda ise se\u00e7me s\u00f6z konusudur. <\/p>\n
\u00dc n kenarl\u0131 d\u00fczg\u00fcn bir \u00e7okgenin k\u00f6\u015fegen say\u0131s\u0131:<\/p>\n
\u00dc Herhangi \u00fc\u00e7\u00fc do\u011frusal olmayan, ayn\u0131 d\u00fczlemde bulunan n tane noktayla;
\na) \u00c7izilebilecek do\u011fru say\u0131s\u0131<\/p>\n
b) K\u00f6\u015feleri bu noktalar \u00fczerinde olan<\/p>\n
tane \u00fc\u00e7gen \u00e7izilebilir.
\n\u00dc Ayn\u0131 d\u00fczlemde birbirine paralel olmayan n tane do\u011fru en \u00e7okfarkl\u0131 noktada kesi\u015firler.
\n\u00dc Ayn\u0131 d\u00fczlemde bulunan do\u011frulardan n tanesi birbirine paralel ve bu n tane do\u011fruya paralel olmayan di\u011fer m tane do\u011fru da birbirine paraleldir.<\/p>\n
D\u00fczlemde kenarlar\u0131 bu do\u011frular \u00fczerinde olan
\ntane paralelkenar olu\u015fur.
\n\u00dc Ayn\u0131 d\u00fczlemde yar\u0131\u00e7aplar\u0131 farkl\u0131 n tane \u00e7emberin en \u00e7ok tane kesim noktas\u0131 vard\u0131r.<\/p>\n
III. B\u0130NOM A\u00c7ILIMI
\nA. TANIM
\n n \u00ce IN olmak \u00fczere,<\/p>\n
ifadesine binom a\u00e7\u0131l\u0131m\u0131 denir.
\n Burada;<\/p>\n
say\u0131lar\u0131na binomun katsay\u0131lar\u0131 denir.<\/p>\n
ifadelerinin her birine terim denir.
\n ifadesinde katsay\u0131, xn \u2013 1 ve yr ye de terimin \u00e7arpanlar\u0131 denir.<\/p>\n
B. (x + y)n A\u00c7ILIMININ \u00d6ZELL\u0130KLER\u0130
\n1) (x + y)n a\u00e7\u0131l\u0131m\u0131nda (n + 1) tane terim vard\u0131r.
\n2) Her terimdeki x ve y \u00e7arpanlar\u0131n\u0131n \u00fcslerinin top-lam\u0131 n dir.
\n3) Katsay\u0131lar toplam\u0131n\u0131 bulmak i\u00e7in de\u011fi\u015fkenler yerine 1 yaz\u0131l\u0131r. Buna g\u00f6re, (x + y)n nin katsay\u0131lar\u0131n\u0131n toplam\u0131 (1 + 1)n = 2n dir.
\n4) (x + y)n ifadesinin a\u00e7\u0131l\u0131m\u0131 x in azalan kuvvetlerine g\u00f6re dizildi\u011finde;
\n ba\u015ftan (r + 1). terim :
\n sondan (r + 1). terim :
\n(x \u2013 y)n ifadesinin a\u00e7\u0131l\u0131m\u0131nda 1. terimin i\u015fareti (+), 2. terimin i\u015fareti (\u2013), 3. terimin i\u015fareti (+) … d\u0131r.
\nK\u0131saca; y nin \u00fcss\u00fc \u00e7ift say\u0131 olan terimin i\u015fareti (+), tek say\u0131 olan terimin i\u015fareti (\u2013) dir.
\n\u00dc n \u00ce N+ olmak \u00fczere,
\n (x + y)2n nin a\u00e7\u0131l\u0131m\u0131nda ortanca terim<\/p>\n
\u00dc n \u00ce IN+ olmak \u00fczere,
\n (xm + )n a\u00e7\u0131l\u0131m\u0131ndaki sabit terim,
\n ifadesinde m . (n \u2013 r) \u2013 kr = 0 ko\u015fulunu sa\u011flayan n ve r de\u011ferleri yaz\u0131larak bulunur.
\n\u00dc c bir ger\u00e7el say\u0131 olmak \u00fczere, (x + y + c)n a\u00e7\u0131l\u0131m\u0131ndaki sabit terimi bulmak i\u00e7in
\n x = 0 ve y = 0 yaz\u0131l\u0131r.
\n\u00dc (a + b + c)n nin a\u00e7\u0131l\u0131m\u0131nda
\n ak . br . cm li terimin katsay\u0131s\u0131;<\/p>\n","protected":false},"excerpt":{"rendered":"
I. PERM\u00dcTASYON A. SAYMANIN TEMEL KURALI 1) Ayr\u0131k iki i\u015flemden biri m yolla, di\u011feri n yolla yap\u0131labiliyorsa, bu i\u015flemlerden biri veya di\u011feri m + n yolla yap\u0131labilir. 2) \u0130ki i\u015flemden birincisi m yolla yap\u0131labiliyorsa ve ilk i\u015flem bu m yoldan birisiyle yap\u0131ld\u0131ktan sonra ikinci i\u015flem n yolla yap\u0131labiliyorsa bu iki i\u015flem birlikte m . n …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1404,1403],"tags":[7212,7346,7345,7303,7304],"class_list":["post-3130","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-binom-acilimi","tag-duzlem","tag-faktoriyel","tag-kombinasyon","tag-permutasyon"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3130","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/comments?post=3130"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3130\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3130"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3130"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3130"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}