📘 combinatorics

1. Soal pertama: Banyak bilangan 4 angka berbeda lebih dari 4000 dari angka 2, 3, 4, 5, 6, 7. - Syarat: angka pertama harus 4, 5, 6, atau 7 agar > 4000.

1. The problem asks: How many 4-digit numbers greater than 4000 can be formed using the digits 2, 3, 4, 5, 6, and 7, with all digits different? 2. To solve this, we use the countin

1. **State the problem:** A restaurant menu has 3 sandwiches, 4 drinks, and 5 desserts. We want to find how many unique meals are possible if a meal consists of one item from each

1. **State the problem:** Julius wants to know how many different meal combinations he can have if he chooses one dish from each course: appetizer, main course, and dessert. 2. **F

1. **State the problem:** Edwin wants to buy three vehicles: a car, a truck, and a motorcycle. Each vehicle has specific color options. 2. **List the options:**

1. **Problem:** Find the generating function for $a_r$, the number of integer solutions to $e_1 + e_2 = r$ with $e_1 \in \{0,3,4,8\}$ and $e_2 \in \{0,4,5,8\}$. **Step 1:** The gen

1. **Problem:** Determine a generating function for the sequence $a_r$ given by the number of integer solutions to the equation $$e_1 + e_2 = r$$ with $$e_1 \in \{0,3,4,8\}$$ and $

1. **Problem statement:** We want to find the number of distinct paths from point $(0,0)$ to point $(3,3)$ on a grid, where movement is allowed only to the right, upward, or diagon

1. **Problem Statement:** We need to find the number of different paths from the bottom-left corner to the top-right corner of a 6 × 6 grid, moving only right or up, without crossi

1. **State the problem:** We have 24 points placed around a circle, and we want to find how many line segments are drawn between every pair of points. 2. **Formula used:** The numb

1. **Problem:** How many handshakes occur if eight people each shake hands with every other person exactly once? 2. **Formula:** The number of handshakes among $n$ people is given

1. The problem states that a teacher has 5 different pets and 16 volunteers out of 75 students. 2. The teacher will select 5 volunteers to take 1 pet each.

1. **Problem Statement:** Karla has 6 questions and wants to find out how many unique ways she can arrange these 6 questions in different orders. 2. **Formula Used:** The number of

1. **Énoncé du problème :** Calculer les valeurs suivantes :

1. The problem is to understand the meaning and properties of the binomial coefficient $\binom{n}{k}$. 2. The binomial coefficient $\binom{n}{k}$ represents the number of ways to c

1. **Problem statement:** We have an infinite chessboard with an $n$-coloring: one green square, one blue square, and $n$ red squares.

1. Masalah: Hitung banyak susunan berbeda dari huruf-huruf kata MISSISSIPPI dengan syarat dua huruf P tidak boleh berdampingan. 2. Huruf-huruf dalam MISSISSIPPI adalah: M(1), I(4),

1. **Problem Statement:** Woodland College has two rows of 8 seats each (total 16 seats). There are 12 people to be seated. Among them, 3 want to sit in the first row and 6 refuse

1. **Problem statement:** We want to find the number of ways to distribute six indistinguishable objects into four indistinguishable boxes such that each box contains at least one

1. **Problem Statement:** Identify pairs of combinations from the given list that have exactly 4 numbers in common. 2. **Approach:** To find pairs with exactly 4 numbers in common,

1. **Problem statement:** Find the position of the word "science" among all its permutations when arranged in alphabetical order. 2. **Formula and rules:** The total number of perm