📘 combinatorics

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

1. Problem a: Find the number of committees of 5 members from 8 women and 4 men with at most 2 men. - "At most 2 men" means 0, 1, or 2 men.

1. **Problem statement:** We need to find the number of paths a checker can take from the bottom-center position to the top of the board, moving only diagonally upward. The checker

1. The problem involves analyzing a grid with blocked squares marked by "X" and a red circle indicating a position on the board. 2. The grid has 8 columns and 6 rows, with blocked

1. **Define terms with examples:** 1. Permutation: An arrangement of objects in a specific order. Example: Arranging 3 books on a shelf in order (ABC, ACB, BAC, etc.).

1. **Define terms:** 1.a. Permutation: An arrangement of objects in a specific order. Example: Arranging 3 books on a shelf in order.

1. **Problem Statement:** We need to find the number of arrangements of the word "ABSOLUTE" (8 distinct letters) such that the word starts with a vowel (A, E, O, or U) and ends wit

1. **Difference between permutations and combinations:** Permutations consider the order of selection important, while combinations do not.

1. **Problem statement:** We want to find the number of nondecreasing sequences of natural numbers \(\langle a_1, a_2, \ldots, a_k \rangle\) with sum 49 that are *not* good. A sequ

1. **Problem statement:** Find the number of 4-digit numbers formed from digits 0,1,2,3,4,5,6,7 such that each number contains the digit 1 at least once. 2. **Total 4-digit numbers