C# Coding Test Course, Understanding Combinations

In coding tests, one often encounters combinatorial problems such as combinations. A combination refers to the number of ways to select elements from a given set without considering the order of the elements. In this course, we will deepen our understanding of the concept of combinations and learn how to solve these problems using C#.

1. Definition of Combination

A combination refers to the number of ways to select r elements from n elements. The number of combinations can be calculated using the following formula:

C(n, r) = n! / (r! * (n – r)!)

Here, n! denotes the factorial of n, which means n × (n-1) × (n-2) × … × 1. r! and (n – r)! are the factorials of r and (n – r), respectively.

2. Example of Combination Problem

Below is a problem related to combinations.

Problem: Team Formation

There are 5 students. We want to select 3 students to form a team. Calculate the number of possible teams. Note that each student has a unique number, and students are distinguished by their numbers. For example, a team consisting of students 1, 2, and 3 is considered the same as a team consisting of students 2, 1, and 3.

3. Problem Solving Process

3.1 Clarifying the Problem

Let’s break down the problem. We will be selecting 3 out of 5 students. We can solve this issue using the combination formula.

3.2 Specifying Parameters

In this problem:

n = 5 (total number of students)
r = 3 (number of students to select)

3.3 Calculating the Number of Combinations

Let’s calculate the number of combinations using the combination formula.

C(5, 3) = 5! / (3! * (5 – 3)!) = 10

Thus, the total number of possible teams is 10.

4. Implementing in C#

Now, let’s implement the above combination formula in C#.


using System;

class Program
{
    static void Main(string[] args)
    {
        int n = 5; // total number of students
        int r = 3; // number of students to select
        Console.WriteLine("Number of ways to form a team: " + Combination(n, r));
    }

    // Method to calculate combinations
    static int Combination(int n, int r)
    {
        return Factorial(n) / (Factorial(r) * Factorial(n - r));
    }

    // Method to calculate factorial
    static int Factorial(int num)
    {
        if (num <= 1)
            return 1;
        return num * Factorial(num - 1);
    }
}

In the code above, we define the 'Combination' method to calculate combinations and the 'Factorial' method to calculate factorials. When this code is executed, it will output 10, which is the number of ways to form a team.

5. Various Use Cases

Combinations can be used in various situations:

Team formation: It can be used when forming a team with a certain number of members.
Combination games: Useful for strategizing through card combinations in card or board games.
Data sampling: Combinations are used when selecting samples from large datasets.

6. Conclusion

The concept of combinations plays an important role in coding tests and can be used to solve various problems. Through this course, we learned the basics of combinations and how to solve simple problems using C#. In the future, try taking on more complex combination problems.

7. Practice Problems

Practice combinations with the following exercises.

Problem 1: Find the number of ways to select 4 out of 8 friends.
Problem 2: Find the number of ways to select 2 out of 7 cards.

It will also be a good practice to write C# code after solving each problem.

8. Additional Resources

For detailed materials related to combinations, please refer to the following links: