📘 combinatorics

1. **Probleem 1: Hatice gooit met zeven dobbelstenen. Hoeveel mogelijkheden zijn er om in totaal 40 ogen te gooien?** 2. **Formule en regels**

1. The problem is to evaluate the binomial coefficient $\binom{3}{}$, which is incomplete as it lacks the second parameter. 2. The binomial coefficient $\binom{n}{k}$ represents th

1. **State the problem:** We need to find the number of ways to arrange 20 cars in a row where the cars are distinguishable only by their colors. There are 4 blue, 3 black, 5 yello

1. **State the problem:** We want to find how many different five-letter codes can be made using the letters \(a, b, c, d, e\). Then, we want to find how many of these codes start

1. **Problem Statement:** We have ID numbers starting with letter S, followed by 2 digits for the year, then 6 digits.

1. **Stating the problem:** We have a menu with 4 entrée options (Burger, Taco, Rice, Spaghetti), 2 snack options (Chips, Apple), and 2 drink options (Water, Milk).

1. **Problem statement:** We have two girls (Arta, Besa) and three boys (Dioni, Ermiri, Flamur) who want to sit in a row of five seats such that the girls sit next to each other an

1. **Stating the problem:** Dominik has a 3×3 grid with a 2×2 shaded block in the bottom right corner. He wants to place a dark and a light stone so that they are not in the same r

1. **Stating the problem:** We need to find how many different routes can be chosen following the indicated arrow directions while avoiding the black stones. 2. **Understanding the

1. **Stating the problem:** We want to find the number of ways to choose 5 candies from 4 flavours: orange, grape, lemon, and mint. This is a problem of combinations with repetitio

1. **Problem statement:** We have ID numbers starting with letter S, followed by 2 digits representing a year, then 6 digits.

1. **Problem Statement:** We want to find the number of ways to divide 30 people into 6 groups, each containing exactly 5 people. 2. **Assumptions:** We assume that the groups are

1. **Problem statement:** We have a 3×3 grid with the middle square shaded out. The digits 1 to 8 are placed in the grid once each to form four three-digit numbers: two read left-t

1. **Problem:** A selection in which the order of choice is important is known as? 2. **Explanation:** When order matters in selection, the concept used is called a permutation.

1. **Problem:** A selection in which the order of choice is important is known as what? 2. **Formula and Explanation:** When order matters, the selection is called a permutation.

1. The problem gives four values for permutations of letters B, D, C, A: (BDCA) = 100, (BDAC) = 120, (CDAB) = 130, (ADCB) = 150. 2. We need to understand what these values represen

1. The problem is to evaluate the binomial coefficient $\binom{1}{2}$. 2. The binomial coefficient $\binom{n}{k}$ is defined as $\frac{n!}{k!(n-k)!}$ where $n!$ is the factorial of

1. The problem asks which group of shirt colors and bottom styles produces exactly 6 different combinations. 2. The formula to find the total number of combinations when pairing on

1. **State the problem:** We want to find the number of ways to arrange two games of doubles tennis from a group of eight players. 2. **Understand the problem:** Each doubles game

1. **Problem statement:** We have 20 books on a shelf, including 2 red-covered books that must not be placed next to each other. We want to find the number of ways to arrange all 2

1. **Problem statement:** Find the number of distinguishable permutations of the letters "AAABBBCC". 2. **Formula:** The number of distinguishable permutations of $n$ objects where