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Ketua angkatan jurusan TI hanya 1 orang (pria atau wanita, tidak bias gender). Jumlah pria = 65 orang dan jumlah wanita = 15 orang. Berapa banyak cara memilih ketua angkatan? Penyelesaian: 65 + 15 = 80 cara. Contoh 2. Dua orang perwakilan mahasiswa TI mendatangai Ibu Dosen untuk protes nilai ujian. Wakil yang dipilih 1 orang pria dan 1 orang wanita. Berapa banyak cara memilih 2 orang wakil tesrebut? Penyelesaian: 65 15 = 975 cara.  Z% Z Z Z Z& Z Z "" "" "" """  0         @Eff؂oy___PPT10Y+D=' = @B +" `(  `i ` l?6Slide Number Placeholder 5` M<4___PPT9  x*$( d   A `  r&0e0eRectangle 2   {!Perluasan Kaidah Dasar Menghitung" "c$!     `  <(0e0eRectangle 3Rectangle: Click to edit Master text styles Second level Third level Fourth level Fifth level0  br Misalkan ada n percobaan, masing-masing dg pi hasil 1. Kaidah perkalian (rule of product) p1 p2 & pn hasil 2. Kaidah penjumlahan (rule of sum) p1 + p2 + & + pn hasil      (     (   (    (#     (  (  (     @Eff؂oy___PPT10Y+D=' = @B +" h(  hi h l?6Slide Number Placeholder 5` M<4___PPT9  x*$( d    h  r$0e0eRectangle 2   <     h  <0e0eRectangle 3Rectangle: Click to edit Master text styles Second level Third level Fourth level Fifth level0  jContoh 3. Bit biner hanya 0 dan 1. Berapa banyak string biner yang dapat dibentuk jika: (a) panjang string 5 bit (b) panjang string 8 bit (= 1 byte) Penyelesaian: (a) 2 2 2 2 2 = 25 = 32 buah (b) 28 = 256 buahfX Z? Z Z9 Z  '  .              ( ( $  8    @Eff؂oy___PPT10Y+D=' = @B +"P g_pG(  pi p l?6Slide Number Placeholder 5` M<4___PPT9  x*$( d    p  <0e0eRectangle 3Rectangle: Click to edit Master text styles Second level Third level Fourth level Fifth level  "Contoh 4. Berapa banyak bilangan ganjil antara 1000 dan 9999 (termasuk 1000 dan 9999 itu sendiri) yang (a) semua angkanya berbeda (b) boleh ada angka yang berulang. Penyelesaian: (a) posisi satuan: 5 kemungkinan angka (1, 3, 5, 7, 9) posisi ribuan: 8 kemungkinan angka (1 sampai 9) posisi ratusan: 8 kemungkinan angka (0 sampai 9) posisi puluhan: 7 kemungkinan angka (sisa angka yang telah dipakai pada posisi ribuan, ratusan, dan satuan) Banyak bilangan ganjil seluruhnya = (5)(8)(8)(7) = 2240 buah. (b) posisi satuan: 5 kemungkinan angka (yaitu 1, 3, 5, 7 dan 9); posisi ribuan: 9 kemungkinan angka (1 sampai 9) posisi ratusan: 10 kemungkinan angka (0 sampai 9) posisi puluhan: 10 kemungkinan angka (0 sampai 9) Banyak bilangan ganjil seluruhnya = (5)(9)(10)(10) = 4500 h ZQ Z9 Z1 Z "" "k"H  9   ?      @Eff؂oy___PPT10Y+D=' = @B +" x(  xi x l^?6Slide Number Placeholder 5` M<4___PPT9  x*$( d    x  <R0e0eRectangle 3Rectangle: Click to edit Master text styles Second level Third level Fourth level Fifth level  kContoh 5. Sandi-lewat (password) sistem komputer panjangnya 6 sampai 8 karakter. Tiap karakter boleh berupa huruf atau angka; huruf besar dan huruf kecil tidak dibedakan. Berapa banyak sandi-lewat yang dapat dibuat? Penyelesaian: Jumlah karakter password = 26 (A-Z) + 10 (0-9) = 36 karakter. Jumlah kemungkinan sandi-lewat dengan panjang 6 karakter: (36)(36)(36)(36)(36)(36) = 366 = 2.176.782.336 Jumlah kemungkinan sandi-lewat dengan panjang 7 karakter: (36)(36)(36)(36)(36)(36)(36) = 367 = 78.364.164.096 umlah kemungkinan sandi-lewat dengan panjang 8 karakter: (36)(36)(36)(36)(36)(36)(36)(36) = 368 = 2.821.109.907.456 Jumlah seluruh sandi-lewat (kaidah penjumlahan) adalah 2.176.782.336 + 78.364.164.096 + 2.821.109.907.456 = 2.901.650.833.888 buah.  Z Z Zq "  Zv "  Z """" ""*p"*s"*"     @Eff؂oy___PPT10Y+D=' = @B +"  }(  i  lQ?6Slide Number Placeholder 5` M<4___PPT9  x*$( d   6   rU0e0eRectangle 2 @p   pPrinsip Inklusi-Eksklusi a      ZA ??Object 5 `  @Eff؂oy___PPT10Y+D=' = @B +"w   n(  i  l?6Slide Number Placeholder 5` M<4___PPT9  x*$( d   '   r0e0eRectangle 2   a Permutasi  a       ZA ??Object 4    @Eff؂oy___PPT10Y+D=' = @B +"H  _W@?(  i  l3?6Slide Number Placeholder 5` M<4___PPT9  x*$( d     ZA ??Object 4p,  @Eff؂oy___PPT10Y+D=' = @B +"    `(  i  l7?6Slide Number Placeholder 5` M<4___PPT9  x*$( d   8   <50e0eRectangle 3Rectangle: Click to edit Master text styles Second level Third level Fourth level Fifth level` bZ___PPT9<4 >|Definisi: Permutasi adalah jumlah urutan berbeda dari pengaturan objek-objek. Permutasi merupakan bentuk khusus aplikasi kaidah perkalian. Misalkan jumlah objek adalah n, maka urutan pertama dipilih dari n objek, urutan kedua dipilih dari n  1 objek, urutan ketiga dipilih dari n  2 objek, & urutan terakhir dipilih dari 1 objek yang tersisa. Menurut kaidah perkalian, permutasi dari n objek adalah n(n  1) (n  2) & (2)(1) = n!n  ] """"""$"")""C","""""""""""  0N  P       @Eff؂oy___PPT10Y+D=' = @B +"|  s(  i  l5?6Slide Number Placeholder 5` M<4___PPT9  x*$( d      <0e0eRectangle 3Rectangle: Click to edit Master text styles Second level Third level Fourth level Fifth level  : Contoh 6. Berapa banyak  kata yang terbentuk dari kata  HAPUS ? Penyelesaian: Cara 1: (5)(4)(3)(2)(1) = 120 buah kata Cara 2: P(5, 5) = 5! = 120 buah kata Contoh 7. Berapa banyak cara mengurutkan nama 25 orang mahasiswa? Penyelesaian: P(25, 25) = 25! A _ B $  "9" "4""" ":" """"0         @Eff؂oy___PPT10Y+D=' = @B +".  E=%(  i  lܖ?6Slide Number Placeholder 5` M<4___PPT9  x*$( d   y   r0e0eRectangle 2   Permutasi r dari n elemen^  "("("("("("(    ]   <0e0eRectangle 3Rectangle: Click to edit Master text styles Second level Third level Fourth level Fifth levelP  Ada enam buah bola yang berbeda warnanya dan 3 buah kotak. Masing-masing kotak hanya boleh diisi 1 buah bola. Berapa jumlah urutan berbeda yang mungkin dibuat dari penempatan bola ke dalam kotak-kotak tersebut? Penyelesaian: kotak 1 dapat diisi oleh salah satu dari 6 bola (ada 6 pilihan); kotak 2 dapat diisi oleh salah satu dari 5 bola (ada 5 pilihan); kotak 3 dapat diisi oleh salah satu dari 4 bola (ada 4 pilihan). 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