📘 combinatorics

1. **State the problem:** Calculate the combination with repetition for $n=28$ and $r=13$. 2. **Formula:** The formula for combinations with repetition is $$\binom{n+r-1}{r} = \fra

1. **State the problem:** Calculate the combination formula given by $$\frac{(n+r-1)!}{r!(n-1)!}$$ for the values $n=35$ and $r=10$.

1. Masalah: Diberikan angka 0, 1, 3, 4, 5, 7, dan 8. Tentukan banyaknya bilangan genap tiga angka berbeda yang dapat disusun dari angka-angka tersebut. 2. Bilangan genap berarti an

1. The problem asks for the number of permutations of the digits 5, 4, 3, and 2. 2. A permutation is an arrangement of all the members of a set into some sequence or order.

1. **Problem statement:** We need to find the number of ways a basketball coach can select his first 5 players from a 15-man basketball team. 2. **Formula used:** This is a combina

1. **Stating the problem:** We want to understand permutations, which are arrangements of objects in a specific order. 2. **Formula for permutations:** The number of ways to arrang

1. The problem asks: How many rectangles of all sizes are there in a 3x3 grid of squares? Remember, squares are also rectangles. 2. To find the total number of rectangles in a grid

1. Masalah: Tentukan banyak bilangan genap yang terdiri dari 3 angka berbeda yang tersusun dari angka 2, 3, 4, 6, 7, dan 9. 2. Aturan: Bilangan genap adalah bilangan yang digit ter

1. **State the problem:** We need to find how many different posters can be made using one poster board and one marker. 2. **Identify the given information:** There are 3 different

1. Problem: How many routes are there from the lake to the cabins if a hiker can take 4 trails to the lake and then 3 trails from the lake to the cabins? 2. Formula: The total numb

1. **Problem:** Hendro memiliki 5 baju, 6 celana, dan 3 sepatu. Berapa banyak cara Hendro memasangkan pakaian yang dimilikinya? 2. **Formula:** Untuk menghitung banyak cara memasan

1. **Problem statement:** There are 40 members in a club including Ranuf and Saed. 35 members will travel in a coach and 5 in a car. Ranuf must be in the coach and Saed must be in

1. **Problem statement:** We have 400 students with scores from 0 to 10. For part (a), we know for each $i \in \{1,2,3,4,5\}$, the number of students scoring $i+5$ is 2 more than t

1. The problem is to calculate the combination $C(3,10)$, which represents the number of ways to choose 3 items from 10 without regard to order. 2. The formula for combinations is:

1. The problem is to evaluate the expression involving combinations: $$8C_0 \cdot 12C_4 + 8C_1 \cdot 12C_3 + 8C_2 \cdot 12C_2$$ which represents selecting groups from two sets. 2.

1. **Problem statement:** You want to buy 5 movies in total: 3 sci-fi and 2 western. The store has 12 sci-fi movies and 8 western movies. How many ways can you choose these movies?

1. The problem is to find the number of ways to choose 3 items from a set of $n$ items using combinations. 2. The formula for combinations (choosing $k$ items from $n$ without rega

1. **Problem statement:** Twelve people (7 Canadians and 5 Australians) apply for 5 jobs at a ski resort. We want to find the number of ways to award these jobs under different con

1. **Problem statement:** How many different identification codes can be made if the code consists of 2 numbers followed by 5 letters, the code cannot begin with 0, cannot contain

1. **Problem statement:** At Santa’s workshop, each Elf's ID consists of 2 numbers followed by 5 letters. The code cannot begin with 0, cannot contain the letter O, and no repetiti

1. The problem is to understand and solve questions related to permutations and combinations. 2. Permutations refer to the arrangement of objects where order matters, and combinati