📘 combinatorics

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

1. Masalah: Tentukan banyaknya kata 6 huruf yang disusun dari huruf E, M, dan C, dengan syarat setiap huruf harus muncul minimal sekali. 2. Formula yang digunakan adalah prinsip pe

1. **Problem Statement:** A voter can choose among candidates for three positions:

1. **Stating the problem:** Jelena wants to place the letters A, B, C, and D into a 2 × 4 grid such that each letter appears exactly once in each row and in each 2 × 2 sub-square.

1. **Problem Statement:** We have 6 planes parked on a rotating turntable with positions numbered 1 to 6. The turntable can be rotated left (◀) or right (▶) by one position per but

1. Problem: There are 18 mathematics majors and 325 computer science majors. a) How many ways to pick two representatives so that one is a mathematics major and the other is a comp

1. **Problem Statement:** We have 6 distinct letters and 6 corresponding envelopes. We want to find the number of ways to place exactly 3 letters in their correct envelopes and the

1. **State the problem:** We need to find the number of ways to arrange 3 math books, 5 chemistry books, and 7 physics books on a shelf such that all books of the same subject are

1. **State the problem:** We want to find the number of ways to order the letters of the word KITCHEN such that the first letter is a consonant and the last letter is a vowel. 2. *

1. **State the problem:** We want to find the number of ways to arrange the letters of the word "AFRICA" such that the consonants are separated by at least one vowel. 2. **Identify

1. **State the problem:** We want to find the number of arrangements of the digits 2, 4, 5, 5, 6, 6, and 7 that form an even number greater than 6000000. 2. **Analyze the condition

1. The problem asks: In how many ways can you choose 2 cards out of 3 playing cards? 2. This is a combination problem where order does not matter.

1. **Stating the problem:** We want to understand the difference between permutations and combinations, and then find how many ways to select 4 students from 10 and how many ways t