Number of n digit numbers that do not contain 9

Last Updated : 27 Apr, 2021

Given a number n, find how many n digit number can be formed that does not contain 9 as it’s digit.
Examples:

Input : 1
Output : 8
Explanation :
Except 9, all numbers are possible

Input : 2
Output : 72
Explanation :
Except numbers from 90 - 99 and all
two digit numbers that does not end
with 9 are possible.

Total numbers of n digit number that can be formed will be 9*10^(n-1) as except first position all digits can be filled with 10 numbers (0-9). If a digit 9 is eliminated from the list then total number of n digit number will be 8*9^(n-1).
Below is the implementation of above idea:

C++

// CPP program to find number of n
// digit numbers that do not
// contain 9 as it's digit
#include <bits/stdc++.h>
using namespace std;
 
// function to find number of
// n digit numbers possible
int totalNumber(int n)
{
    return 8*pow(9, n - 1);
}
 
// driver function
int main()
{
    int n = 3;
    cout << totalNumber(n);
    return 0;
}

Java

// Java program to find number of 
// n digit numbers that do not
// contain 9 as it's digit
import java.io.*;
 
public class GFG
{
     
// function to find number of
// n digit numbers possible
static int totalNumber(int n)
{
    return 8 * (int)Math.pow(9, n - 1);
}
 
    // Driver Code
    static public void main (String[] args)
    {
        int n = 3;
        System.out.println(totalNumber(n));
         
    }
}
 
// This code is contributed by vt_m.

Python3

# python program to find number of n
# digit numbers that do not
# contain 9 as it's digit
 
# function to find number of
# n digit numbers possible
def totalNumber(n):
     
    return 8 * pow(9, n - 1);
  
# driver function
n = 3
print(totalNumber(n))
 
# This code is contributed by Sam007

C#

// C# program to find number of 
// n digit numbers that do not
// contain 9 as it's digit
using System;
 
public class GFG
{
     
// function to find number of
// n digit numbers possible
static int totalNumber(int n)
{
    return 8 * (int)Math.Pow(9, n - 1);
}
 
    // Driver Code
    static public void Main ()
    {
        int n = 3;
        Console.WriteLine(totalNumber(n));
         
    }
}
 
// This code is contributed by vt_m.

php

<?php
// php program to find number of n
// digit numbers that do not
// contain 9 as it's digit
 
// function to find number of
// n digit numbers possible
function totalNumber($n)
{
    return 8 * pow(9, $n - 1);
}
  
// driver function
$n = 3;
print(totalNumber($n))
 
// This code is contributed by Sam007
?>

Javascript

<script>
 
// Javascript program to find number of 
// n digit numbers that do not
// contain 9 as it's digit
 
// function to find number of
// n digit numbers possible
function totalNumber(n)
{
    return 8 * Math.pow(9, n - 1);
}
   
// Driver code
        let n = 3;
        document.write(totalNumber(n));
    
   // This code is contributed by code_hunt.
</script>

Output:

This article is contributed by Dibyendu Roy Chaudhuri. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.

My Personal Notes

Related Articles

Number of n digit numbers that do not contain 9

C++

Java

Python3

C#

php

Javascript