Finding non-bouncy numbers under 10^x

I am trying to find non bouncy numbers under \$10^x\$ where \$1\le x\le 1000\$.
\$123456\$ is an increasing number where every digit is greater than or equal to the previous digit (\$1223344\$ is also counted as an increasing number).
Similarly a decreasing number is one where every digit is smaller than or equal to the previous digit (\$443322\$ is also counted as an decreasing number).

155224 such numbers, which are neither increasing, nor decreasing, are bouncy numbers, such that 12951 numbers below one-million that are not bouncy. I want to find number of non bouncy number under \$10^x\$.

My code works perfectly fine, but when \$n\$ is greater than 7, it takes way too much time to give the output! So, it needs performance optimizations.

import java.util.*;
class A{
static String s;
public static void main(String z[]){
    int n,i;
    Scanner sc=new Scanner(System.in);
    n=sc.nextInt();
    int input[]=new int[n];
    int output[]=new int[n];
    for(i=0;is.charAt(i+1)){
             return false;
         }
    }
return true;    
}
public static boolean isDecreasing(String s){
     int len=s.length();
     for(int i=0;i<len-1;i++){
         if(s.charAt(i)<s.charAt(i+1)){
             return false;
         }
    }
return true;
}
public static int noOfBouncy(int k){
int limit=(int)Math.pow(10,k);
int count=0;
int num=1;
while(num<limit){
    s=new String(Integer.toString(num));
    if(isIncreasing(s) || isDecreasing(s) ){
    }
    else{
       count++;
    }
    num++;
  }
count=limit-count;
return count-1; 
}
}

This is not a review but an expanded comment.

Brute force is bad. Do some math first.

Consider a non-decreasing number of length \$n\$ formed by exactly \$k\$ given digits. It has exactly \$k - 1\$ transitions from a digit to a larger one, and there are exactly \$n - 1\$ places where the transition may happen, so there are \$\binom{n-1}{k-1}\$ such numbers. The \$\binom{10}{k}\$ ways to pick \$k\$ digits give a subtotal of \$\binom{n-1}{k-1}\binom{10}{k}\$, and a grand total is \$\sum_{k=1}^{10}\binom{n-1}{k-1}\binom{10}{k}\$.

So the problem nails down to efficient calculation of binomial coefficients, which in this case is fairly straightforward, since you never need more than 10 factors.

StackExchange Code Review Q#110450, answer score: 11