📘 combinatorics

1. **State the problem:** Calculate the value of $\binom{400}{2} \times 500$. 2. **Recall the formula for combinations:**

1. The problem is to select three questions from each difficulty level: easy, medium, and hard. 2. This is a combinatorial selection problem where we choose 3 items from each categ

1. The problem asks if letters and numbers can repeat in a given context. 2. To answer this, we need to understand the concept of repetition in combinatorics or arrangements.

1. **Problem Statement:** We need to find how many unique license plates can be formed with the format of three numbers followed by three letters, where both numbers and letters ca

1. **Problem statement:** Find the number of 5-digit odd numbers that can be formed with no repeated digits. 2. **Key points:**

1. **Problem statement:** We have 7 shortlisted applicants and 3 different internship roles. We want to find how many different ways the roles can be assigned when the order of app

1. **State the problem:** We want to find how many CVC (consonant–vowel–consonant) syllables can be formed using 10 consonants and 4 vowels. 2. **Formula and explanation:** The num

1. **Stating the problem:** We want to find the total number of combinations possible from a set of items. 2. **Formula used:** The number of combinations of choosing $k$ items fro

1. **Problem Statement:** We need to find the number of different combinations of candies taken from a bowl containing 7 identical kiwi, 10 identical cherry, and 7 identical orange

1. **Problem statement:** We have a circle divided into 6 sectors, each painted either red, green, or blue, with exactly 2 sectors of each color. We want to find the number of ways

1. The problem asks: How many different colorings are possible? We need more context to solve this, such as the number of objects to color and the number of colors available. 2. Ty

1. **Problem Statement:** We have a circle divided into 6 sectors of different sizes. We want to paint 2 sectors red, 2 green, and 2 blue such that no two adjacent sectors share th

1. **Problem:** Wie viele dreiziffrige Zahlen kann man aus den Ziffern 3, 5, 6 und 8 bilden? 2. **Formel:** Ziehen mit Zurücklegen, Anzahl der Möglichkeiten ist $n^k$, wobei $n$ di

1. **Problem statement:** 7a) Calculate the number of ways to assign 4 different light bulbs to 4 specific lamp sockets.

1. The problem is to find the number of combinations of 52 items taken 2 at a time, denoted as $52 \choose 2$. 2. The formula for combinations is:

1. **Problem Statement:** We need to find the number of possible special plate numbers consisting of 3 letters followed by 2 digits.

1. **Problem Statement:** We need to find the number of possible special plate numbers made up of 3 letters followed by 2 digits.

1. **Problem Statement:** We want to find the number of ways to arrange 6 red roses and 4 white roses in a garland such that all 4 white roses are together. 2. **Understanding the

1. **Problem statement:** If 12 people each shake hands with every other person exactly once, how many handshakes occur in total? 2. **Formula used:** The number of handshakes amon

1. **Problem Statement:** Find the number of distinct arrangements of the letters in the word ABRACADABRA. 2. **Understanding the problem:** The word ABRACADABRA has 11 letters wit

1. **Problem statement:** We need to find the number of ways to select 3 gifts from a list of 20 possible wedding presents. 2. **Formula used:** This is a combination problem becau