Rudi ingin membuat nomor undian peserta gerak jalan yang terdiri dari gabungan namanya dan angka-angka yang terdiri dari 5 angka ( a, b, c, d, e ) dimana a adalah urutan angka pertama, b angka kedua, c angka ketiga, d angka keempat, dan e angka kelima, dengan ketentuan a < b < c < d < e, sedangkan nama Rudi tercantum di awal atau di akhir. Contoh RUDI23456, 14789RUDI. Banyak undian yang dapat dibuat Rudi apabila huruf kapital dan huruf kecil tidak dibedakan adalah ....

Halo Krisna, aku bantu jawab ya. Jawaban: 904 Pembahasan: Angka: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Banyak undian untuk posisi angka dan nama rudi ditukar = A = 2 Banyak undian untuk Angka: Perhatikan urutan a < b < c < d < e Misal B = banyak susunan angka jika a = 0, 1, 2, 3, 4, atau 5. Maka b = 6, c = 7, d = 8 dan e = 9 B = 6 C = banyak susunan jika a = 0, 1, 2, 3, atau 4. Maka kemungkinan nilai b , c, d, dan e adalah b = 5, c = 6, d = 7, e = 8 b = 5, c = 6, d = 7, e = 9 b = 5, c = 7, d = 8, e = 9 b = 6, c = 7, d = 8, e = 9 Sehingga diperoleh: C = 5 x 4 = 20 D = banyak susunan jika a = 0, 1, 2, atau 3 Maka kemungkinan nilai b, c, d, dan e adalah b = 4, c = 5, d = 6, e = 7 b = 4, c = 5, d = 6, e = 8 b = 4, c = 5, d = 6, e = 9 b = 4, c = 5, d = 7, e = 8 b = 4, c = 5, d = 7, e = 9 b = 4, c = 5, d = 8, e = 9 b = 4, c = 6, d = 7, e = 8 b = 4, c = 6, d = 7, e = 9 b = 4, c = 7, d = 8, e = 9 Untuk kemungkinan b = 5 ada 3, b = 6 ada 1, dan b = 4 ada 9, sehingga total kemungkinan untuk nilai b, c, d, dan e adalah 3 + 1 + 9 = 13 D = 4 x 13 = 52 E = banyak susunan jika a = 0, 1, atau 2. Maka kemungkinan nilai b, c, d, dan e adalah b = 3, c = 4, d = 5, e = 6 b = 3, c = 4, d = 5, e = 7 b = 3, c = 4, d = 5, e = 8 b = 3, c = 4, d = 5, e = 9 b = 3, c = 4, d = 6, e = 7 b = 3, c = 4, d = 6, e = 8 b = 3, c = 4, d = 6, e = 9 b = 3, c = 4, d = 7, e = 8 b = 3, c = 4, d = 7, e = 9 b = 3, c = 4, d = 8, e = 9 b = 3, c = 5, d = 6, e = 7 b = 3, c = 5, d = 6, e = 8 b = 3, c = 5, d = 6, e = 9 b = 3, c = 5, d = 7, e = 8 b = 3, c = 5, d = 7, e = 9 b = 3, c = 5, d = 8, e = 9 b = 3, c = 6, d = 7, e = 8 b = 3, c = 6, d = 7, e = 9 b = 3, c = 7, d = 8, e = 9 Untuk kemungkinan b = 3 ada 19, dan b = 4, 5, atau 6 ada 13, sehingga total kemungkinan untuk nilai b, c, d, dan e adalah 19 + 13 = 32 E = 3 x 32 = 96 E = banyak susunan jika a = 0 atau 1 Maka kemungkinan nilai b, c, d, dan e adalah b = 2, c = 3, d = 4, e = 5 b = 2, c = 3, d = 4, e = 6 b = 2, c = 3, d = 4, e = 7 b = 2, c = 3, d = 4, e = 8 b = 2, c = 3, d = 4, e = 9 b = 2, c = 3, d = 5, e = 6 b = 2, c = 3, d = 5, e = 7 b = 2, c = 3, d = 5, e = 8 b = 2, c = 3, d = 5, e = 9 b = 2, c = 3, d = 6, e = 7 b = 2, c = 3, d = 6, e = 8 b = 2, c = 3, d = 6, e = 8 b = 2, c = 3, d = 7, e = 8 b = 2, c = 3, d = 7, e = 9 b = 2, c = 3, d = 8, e = 9 Kemungkinan c = 3 ada 15 Kemungkinan c = 4 ada 10 Kemungkinan c = 5 ada 6 Kemungkinan c = 6 ada 2 Kemungkinan c = 7 ada 1 Kemungkinan b = 2 ada 15 + 10 + 6 + 2 + 1 = 34 Kemungkinan b = 3, 4, 5, atau 6 ada 32 Sehingga total kemungkinan untuk nilai b, c, d, dan e adalah 34 + 32 = 66 E = 2 x 66 = 132 F = banyak susunan jika a = 0 Maka kemungkinan nilai b, c, d, dan e adalah b = 1, c = 2, d = 3, e = 4 b = 1, c = 2, d = 3, e = 5 b = 1, c = 2, d = 3, e = 6 b = 1, c = 2, d = 3, e = 7 b = 1, c = 2, d = 3, e = 8 b = 1, c = 2, d = 3, e = 9 b = 1, c = 2, d = 4, e = 5 b = 1, c = 2, d = 4, e = 6 b = 1, c = 2, d = 4, e = 7 b = 1, c = 2, d = 4, e = 8 b = 1, c = 2, d = 4, e = 9 b = 1, c = 2, d = 5, e = 6 b = 1, c = 2, d = 5, e = 7 b = 1, c = 2, d = 5, e = 8 b = 1, c = 2, d = 5, e = 9 b = 1, c = 2, d = 6, e = 7 b = 1, c = 2, d = 6, e = 8 b = 1, c = 2, d = 6, e = 9 b = 1, c = 2, d = 7, e = 8 b = 1, c = 2, d = 7, e = 9 b = 1, c = 2, d = 8, e = 9 Kemungkinan c = 2 ada 21 Kemungkinan c = 3 ada 15 Kemungkinan c = 4 ada 10 Kemungkinan c = 5 ada 6 Kemungkinan c = 6 ada 2 Kemungkinan c = 7 ada 1 Kemungkinan b = 1, ada 21 + 15 + 10 + 6 + 2 + 1 = 55 Kemungkinan b = 2, 3, 4, 5, atau 6 ada 66 Sehingga total kemungkinan untuk nilai b, c, d, dan e adalah 55 + 66 = 121 F = 2 x 121 = 242 Total kemungkinan = A x ( B + C + D + E + F) = 2 x (6 + 20 + 52 + 132 + 242) = 2 x 452 = 904 Dengan demikian diperoleh banyak undian yang dapat dibuat Rudi adalah 904. Semoga membantu ya 😊