📘 combinatorics

1. **Problem:** How many different words can be formed with the letters of the word "MISSISSIPPI"? 2. **Step 1: Understand the problem**

1. Masalah: Tentukan banyak permutasi dari angka 1, 2, 3, 4, 5, 6, 7 yang tidak memiliki angka 1 di posisi pertama, tidak memiliki angka 4 di posisi keempat, dan tidak memiliki ang

1. **Problem statement:** We have 6 models from 3 continents: 2 from Europe, 2 from South America, and 2 from North America. We want to arrange them so that models from the same co

1. **Problem statement:** We want to find:

1. **Problem statement:** We need to arrange 5 reindeer: Gloopin, Quentin, Ezekiel, Lancer, and one more unnamed reindeer in a single line. 2. **Condition:** Quentin and Gloopin mu

1. **State the problem:** We want to find the number of unique ways to arrange the letters in the word PRETTY. 2. **Identify the letters and their frequencies:** The word PRETTY ha

1. Tentukan banyak solusi dari $x_1 + x_2 + x_3 + x_4 + x_5 + x_6 = 34$ dengan $x_i$ bilangan bulat genap positif dan $x_i \leq 10$.\n\n2. Tentukan banyak solusi dari $x_1 + x_2 +

1. Tentukan banyak solusi dari $x_1 + x_2 + x_3 + x_4 + x_5 + x_6 = 34$ dengan $x_i$ bilangan bulat genap positif dan $x_i \leq 10$.\n\nLangkah 1: Ubah variabel agar lebih mudah di

1. Tentukan banyak solusi dari $x_1 + x_2 + x_3 + x_4 + x_5 + x_6 = 34$ dalam bilangan bulat genap positif yang tidak melebihi 10. 2. Tentukan banyak solusi dari $x_1 + x_2 + x_3 +

1. **Problem statement:** From the digits 1, 2, 2, 3, 4, 5, form 4-digit numbers where each digit is used at most once. Conditions:

1. **Problem:** There are 18 mathematics majors and 325 computer science majors. (a) In how many ways can two representatives be picked so that one is a mathematics major and the o

1. **Problem Statement:** Find the number of 4-digit numbers that do not include the digits 7 and 8, are divisible by 4, and have no repeated digits. 2. **Key Points:**

1. **Problem statement:** From a standard 52-card deck, how many cards must be chosen at random to guarantee having at least three cards of clubs? 2. **Understanding the problem:**

1. **Stating the problem:** We have a deck of 52 cards, and we want to find two things:

1. **Problem statement:** How many ways can 6 people be lined up to get on a bus? 2. **Formula:** The number of ways to arrange $n$ distinct people in a line is $n!$.

1. **Problem Statement:** Calculate the number of possible telephone numbers, dressing combinations, security alarm codes, and four-digit numbers based on given constraints. 2. **T

1. **Problem Statement:** Determine the number of compositions of 1s and 2s that sum up to 18. 2. **Understanding the Problem:** A composition of a number is a way of writing it as

1. **State the problem:** We need to find how many distinct labels are possible for auditorium chairs, where each label consists of one uppercase letter followed by an integer from

1. Masalah: Tentukan berapa banyak bilangan ganjil antara 500 dan 1000 dengan ketentuan (i) semua angkanya berbeda, (ii) boleh ada angka yang berulang. 2. Definisi bilangan ganjil:

1. Masalah: Tentukan berapa banyak bilangan ganjil antara 500 dan 1000 dengan ketentuan (i) semua angkanya berbeda, (ii) boleh ada angka yang berulang. 2. Definisi bilangan ganjil:

1. Тодорхойлолт: 3x3 хэмжээтэй торон дээр гурван өөр хэмжээтэй квадрат зурж болдог гэж өгөгдсөн. 2. Ерөнхий зарчим: n x n хэмжээтэй торон дээр зурж болох квадратуудын тоо нь бүх бо