- C++ Programming Examples
- C++ Programming Examples
- C++: Hello World
- C++: Get Input
- C++: Print Integer
- C++: Add two numbers
- C++: Add, Sub, Multiply, Div
- C++: Add Digits
- C++: Find Average and Percentage
- C++: Find Arithmetic Mean
- C++: Sum of n Natural Numbers
- C++: Sum of n Numbers
- C++: Square's Area and Perimeter
- C++: Rectangle's Area and Perimeter
- C++: Triangle's Area and Perimeter
- C++: Area and Circumference
- C++: Find Simple Interest
- C++: Fahrenheit to Celsius
- C++: Celsius to Fahrenheit
- C++: Print Prime Numbers
- C++: Reverse a Number
- C++: Swap Two Numbers
- C++: Print Multiplication Table
- C++: Find Factorial of a Number
- C++: Find Factors of a Number
- C++: Find HCF and LCM
- C++: Create a Calculator
- C++: Count Digits in a Number
- C++: First and Last Digit Sum
- C++: Product of Number Digits
- C++: Sum of Squares of Digits
- C++: Interchange Digits of Number
- C++ if-else Programs
- C++: Check Even or Odd
- C++: Check Prime or Not
- C++: Check Alphabet or Not
- C++: Check Vowel or Not
- C++: Check Leap Year or Not
- C++: Check Reverse equals Original
- C++: Check Perfect Number
- C++: Check Palindrome or Not
- C++: Check Armstrong or Not
- C++: Divisibility Test
- C++: Find Labor Wage
- C++: Find Discounted Price
- C++: Find Shipping Charge
- C++: Find Telephone Bills
- C++: Calculate Student Grade
- C++: Largest of Two Numbers
- C++: Largest of Three Numbers
- C++ Number Conversion
- C++: Decimal to Binary
- C++: Decimal to Octal
- C++: Decimal to Hexadecimal
- C++: Binary to Decimal
- C++: Binary to Octal
- C++: Binary to Hexadecimal
- C++: Octal to Decimal
- C++: Octal to Binary
- C++: Octal to Hexadecimal
- C++: Hexadecimal to Decimal
- C++: Hexadecimal to Binary
- C++: Hexadecimal to Octal
- C++ Pattern Programs
- C++: Pattern Programs
- C++: Print Diamond Pattern
- C++: Print Floyd's Triangle
- C++: Print Pascal's Triangle
- C++ Array Programs
- C++: 1D Array Program
- C++: Linear Search
- C++: Binary Search
- C++: Largest Element in an Array
- C++: Smallest Element in an Array
- C++: Find Second Largest Element
- C++: Find Second Smallest Element
- C++: Sum of All Elements
- C++: Multiply All Elements
- C++: Element in Even Position
- C++: Element in Odd Position
- C++: Print Even Numbers in Array
- C++: Print Odd Numbers in Array
- C++: Count Even or Odd Numbers
- C++: Sum of Even or Odd Numbers
- C++: Count Positive, Negative, Zero
- C++: Reverse an Array
- C++: Insert an Element
- C++: Delete an Element
- C++: Merge two Arrays
- C++: Bubble Sort
- C++: Selection Sort
- C++: Insertion Sort
- C++: Common Elements
- C++: 2D Array Programs
- C++: Add Two Matrices
- C++: Subtract Two Matrices
- C++: Transpose Matrix
- C++: Multiply Two Matrices
- C++: 3D Array Programs
- C++ String Programs
- C++: Print String
- C++: Find String Length
- C++: Compare Two Strings
- C++: Copy String
- C++: String Concatenation
- C++: Reverse a String
- C++: Delete Vowels from a String
- C++: Delete a Word from a String
- C++: Count Characters in a String
- C++: Count Words in a String
- C++: Frequency of Words
- C++: Remove Spaces from Strings
- C++: Sort a String
- C++: Uppercase to Lowercase
- C++: Lowercase to Uppercase
- C++: Swap Two Strings
- C++: Check the Anagram or Not
- C++: Capitalize All Words in a String
- C++: Get Numbers from a String
- C++ File Programs
- C++: Read a File
- C++: Write Content to a File
- C++: Append Data to a File
- C++: Read and Display File
- C++: Copy a File
- C++: Merge Two Files
- Count Characters in a File
- C++: Capitalize Every Word
- C++: List Files in Directory
- C++: Delete a File
- C++: Encrypt and Decrypt a File
- C++ Misc Programs
- C++: Print ASCII Value
- C++: Add Binary Numbers
- C++: Generate Random Numbers
- C++: Print a Smiling Face
- C++: Days into Years and Months
- C++: Add Two Numbers using Pointer
- C++: Print Fibonacci Series
- C++: Generate Armstrong Numbers
- C++: Find nCr and nPr
- C++: Get IP Address
- C++: Print Date and Time
- C++: Shutdown and Restart Computer
- C++ Programming Tutorial
- C++ Tutorial
C++ Program to Find nPr and nCr
In this article, you will learn and get code to find and print nPr (permutation) and nCr (combination) in the C++ language. Here is the list of programs available in this article:
- Using a while loop, find nPr
- Using a while loop, find nCr
- Find nPr and nCr in a single program
- Using a for loop, calculate nPr and nCr
- Find nPr and nCr using a user-defined function
Before going through these programs, let's understand the formula used to calculate permutation (nPr) and combination (nCr).
nPr Formula
The formula to find the value of nPr is:
nPr = n!/(n-r)!
Note: The symbol (!) indicates factorial.
Note: The permutation (nPr) value shows the number of ways to arrange r things out of n.
nCr Formula
The formula to find the value of nCr is:
nCr = n!/r!(n-r)!
Note: The combination (nCr) value shows the number of ways to select r things out of n.
C++: Find nPr (permutation)
To find nPr in C++ programming, you have to ask the user to enter the values of n and r. In both the program for calculating nPr and nCr, the only required code is to find the factorial of a number. The rest of the things are just normal things like initializing, dividing, printing, etc.
The question is, "Write a program in C++ to find the value of nPr." Here is its answer:
#include<iostream> using namespace std; int main() { long long fact=1, numerator, denominator; int perm, n, r, i=1, sub; cout<<"Enter the Value of n: "; cin>>n; cout<<"Enter the Value of r: "; cin>>r; while(i<=n) { fact = i*fact; i++; } numerator = fact; // n! sub = n-r; fact = 1; i = 1; while(i<=sub) { fact = i*fact; i++; } denominator = fact; // (n-r)! perm = numerator/denominator; cout<<"\nPermutation (nPr) = "<<perm; cout<<endl; return 0; }
This program was built and runs under the Code::Blocks IDE. Here is the sample run:
Now type a number, say 5, as the value of n, and then type another number, say 3, as the value
of r. Now press the ENTER
key to find and print the value of nPr as shown in the output
given below:
There are 60 ways to arrange three things out of five.
The following block of code:
while(i<=n) { fact = i*fact; i++; }
is used to find the factorial of n. So the statement:
numerator=fact;
is used to initialized the factorial of n to the numerator. In other words, numerator = n!
In the above program, the factorial of n and n-r gets calculated, and then using the formula of nPr, its value gets calculated and printed on the output. For more information, consult the factorial program.
C++: Find nCr (combination)
This program asks the user to enter the value of n and r. Based on the values, the program finds and prints the value of nCr, which tells the number of ways to select r things out of n:
#include<iostream> using namespace std; int main() { long long fact=1, numerator, denominator; int comb, n, r, i=1, sub; cout<<"Enter the Value of n: "; cin>>n; cout<<"Enter the Value of r: "; cin>>r; while(i<=n) { fact = i*fact; i++; } numerator = fact; // n! sub = n-r; fact = 1; i = 1; while(i<=sub) { fact = i*fact; i++; } denominator = fact; // (n-r)! fact = 1; i = 1; while(i<=r) { fact = i*fact; i++; } denominator = (fact*denominator); comb = numerator/denominator; cout<<"\nCombination (nCr) = "<<comb; cout<<endl; return 0; }
Here is its sample run with user input, with 5 as the value of n and 3 as the value of r:
There are 10 ways to select 3 things out of 5.
Find nPr and nCr in a Single C++ Program
This program receives the values of n and r. Then it calculates and prints the permutation and combination values for both.
#include<iostream> using namespace std; int main() { long long fact=1, numerator, denominator; int npr, ncr, n, r, i=1, sub; cout<<"Enter the Value of n: "; cin>>n; cout<<"Enter the Value of r: "; cin>>r; while(i<=n) { fact = i*fact; i++; } numerator=fact; // fact = n! sub = n-r; fact=1, i=1; while(i<=sub) { fact = i*fact; i++; } denominator = fact; // fact = (n-r)! npr = numerator/denominator; i=1, fact=1; while(i<=r) { fact = i*fact; i++; } ncr = npr/fact; // fact = r! cout<<"\nPermutation (nPr) = "<<npr; cout<<"\nCombination (nCr) = "<<ncr; cout<<endl; return 0; }
Here is its sample run with the same user input as provided in the above program's sample run:
Using a for loop, calculate nPr and nCr
This program uses a for loop (instead of while) to do the same job as the previous program.
#include<iostream> using namespace std; int main() { long long fact, numerator, denominator; int npr, ncr, n, r, i, sub; cout<<"Enter the Value of n: "; cin>>n; cout<<"Enter the Value of r: "; cin>>r; for(i=1, fact=1; i<=n; i++) fact = i*fact; numerator=fact; // fact = n! sub = n-r; for(i=1, fact=1; i<=sub; i++) fact = i*fact; denominator = fact; // fact = (n-r)! npr = numerator/denominator; for(i=1, fact=1; i<=r; i++) fact = i*fact; ncr = npr/fact; // fact = r! cout<<"\nPermutation (nPr) = "<<npr; cout<<"\nCombination (nCr) = "<<ncr; cout<<endl; return 0; }
This program produces the same output as the previous program.
Using Function, calculate nPr and nCr.
This is the last program of this article and uses some user-defined functions to do the same task as the previous program.
#include<iostream> using namespace std; long long findFact(int); int findNPR(int, int); int findNCR(int, int); int main() { int npr, ncr, n, r; cout<<"Enter the Value of n: "; cin>>n; cout<<"Enter the Value of r: "; cin>>r; npr = findNPR(n, r); ncr = findNCR(n, r); cout<<"\nPermutation (nPr) = "<<npr; cout<<"\nCombination (nCr) = "<<ncr; cout<<endl; return 0; } long long findFact(int num) { int i=1, fact=1; while(i<=num) { fact = i*fact; i++; } return fact; } int findNPR(int n, int r) { long long numerator, denominator; numerator = findFact(n); denominator = findFact(n-r); return (numerator/denominator); } int findNCR(int n, int r) { int npr, ncr; npr = findNPR(n, r); ncr = npr/findFact(r); return ncr; }
The same program in different languages
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