Count of N-digit numbers with all distinct digits

Difficulty Level : Hard
Last Updated : 01 Apr, 2021

Given an integer N, the task is to find the count of N-digit numbers with all distinct digits.
Examples:

Input: N = 1
Output: 9
1, 2, 3, 4, 5, 6, 7, 8 and 9 are the 1-digit numbers
with all distinct digits.
Input: N = 3
Output: 648

Approach: If N > 10 i.e. there will be atleast one digit which will be repeating hence for such cases the answer will be 0 else for the values of N = 1, 2, 3, …, 9, a series will be formed as 9, 81, 648, 4536, 27216, 136080, 544320, … whose N^th term will be 9 * 9! / (10 – N)!.
Below is the implementation of the above approach:

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the factorial of n
int factorial(int n)
{
    if (n == 0)
        return 1;
    return n * factorial(n - 1);
}
 
// Function to return the count
// of n-digit numbers with
// all distinct digits
int countNum(int n)
{
    if (n > 10)
        return 0;
    return (9 * factorial(9)
            / factorial(10 - n));
}
 
// Driver code
int main()
{
    int n = 3;
 
    cout << countNum(n);
 
    return 0;
}

Java

// Java implementation of the approach
class GFG
{
     
    // Function to return the factorial of n
    static int factorial(int n)
    {
        if (n == 0)
            return 1;
        return n * factorial(n - 1);
    }
     
    // Function to return the count
    // of n-digit numbers with
    // all distinct digits
    static int countNum(int n)
    {
        if (n > 10)
            return 0;
        return (9 * factorial(9) /
                    factorial(10 - n));
    }
     
    // Driver code
    public static void main(String []args)
    {
        int n = 3;
        System.out.println(countNum(n));
    }
}
 
// This code is contributed by Srathore

Python3

# Python3 implementation of the approach
 
# Function to return the factorial of n
def factorial(n) :
 
    if (n == 0) :
        return 1;
    return n * factorial(n - 1);
 
# Function to return the count
# of n-digit numbers with
# all distinct digits
def countNum(n) :
    if (n > 10) :
        return 0;
         
    return (9 * factorial(9) //
                factorial(10 - n));
 
# Driver code
if __name__ == "__main__" :
 
    n = 3;
 
    print(countNum(n));
     
# This code is contributed by AnkitRai01

C#

// C# implementation of the approach
using System;
                     
class GFG
{
     
    // Function to return the factorial of n
    static int factorial(int n)
    {
        if (n == 0)
            return 1;
        return n * factorial(n - 1);
    }
     
    // Function to return the count
    // of n-digit numbers with
    // all distinct digits
    static int countNum(int n)
    {
        if (n > 10)
            return 0;
        return (9 * factorial(9) /
                    factorial(10 - n));
    }
     
    // Driver code
    public static void Main(String []args)
    {
        int n = 3;
        Console.WriteLine(countNum(n));
    }
}
 
// This code is contributed by Princi Singh

Javascript

<script>
 
 
// Javascript implementation of the approach
 
// Function to return the factorial of n
function factorial(n)
{
    if (n == 0)
        return 1;
    return n * factorial(n - 1);
}
 
// Function to return the count
// of n-digit numbers with
// all distinct digits
function countNum(n)
{
    if (n > 10)
        return 0;
    return (9 * factorial(9)
            / factorial(10 - n));
}
 
// Driver code
var n = 3;
document.write(countNum(n));
 
// This code is contributed by rutvik_56.
</script>

Output:

Time Complexity: O(n)

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