📘 combinatorics

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

1. **State the problem:** Find the number of distinguishable permutations of the letters in the string "AAABBBCD". 2. **Formula used:** The number of distinguishable permutations o

1. The problem is to find the value of the binomial coefficient $\binom{9}{8}$. 2. The formula for a binomial coefficient is:

1. The problem asks for the value of the binomial coefficient $\binom{8}{9}$. 2. The binomial coefficient $\binom{n}{k}$ is defined as the number of ways to choose $k$ elements fro

1. **Problem:** A license plate must have 2 letters (not I or O) followed by 3 digits. The last digit cannot be zero. How many different plates can be made? 2. **Step 1: Determine

1. **State the problem:** We want to find the total number of possible ice cream combinations given 6 flavors, 4 toppings, and 2 types of cones.

1. **Problem statement:** We start with an unpainted wooden cube. We paint exactly three faces: one red, one blue, and one green. The other three faces remain unpainted. We want to

1. **State the problem:** We want to find all possible outcomes of answering a quiz with five true/false questions. 2. **Understanding the problem:** Each question has 2 possible a

1. The problem is to select 3 random football matches for each member: gb, jkb, Scouse, spurslad from the given fixtures list. 2. The fixtures are divided into leagues: Premier Lea

1. The problem is to select 3 random football matches for each member: gb, jkb, Scouse, and spurslad from the given list of fixtures. 2. Since the problem is about random selection