UVA - 10338 - Mischievous Children

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;

public class Main {

    public static void main(String[] args) throws IOException {
        InputStreamReader isr = new InputStreamReader(System.in);
        BufferedReader br = new BufferedReader(isr);
        StringBuffer sb = new StringBuffer("");
        String m="";
        BigInteger[] arr = new BigInteger[21];
        for (int i = 0; i < 21; i++) {
            arr[i] = BigInteger.ZERO;
        }
        arr[0]=BigInteger.ONE;
        arr[1]=BigInteger.ONE;
        fact(20,arr);

        int cases=Integer.parseInt(br.readLine());
        int let[]=new int[26];
        for(int i=1;i<cases+1;i++) {
            m=br.readLine();
            int x=m.length();
            let=new int[26];
            StringBuilder temp=new StringBuilder(m);
            for(int j=0;j<temp.length();j++){
               let[m.charAt(j)-'A']++;
            }
            BigInteger sum=BigInteger.ONE;
            for(int j=0;j<26;j++){
                if(let[j]>1){
                     sum=sum.multiply(arr[let[j]]);
                }
            }
            BigInteger ans=arr[x].divide(sum);
            sb.append("Data set ").append(i).append(": ").append(ans).append("\n");
        }
        System.out.print(sb);
    }

    static BigInteger fact(int x, BigInteger[] arr) {
        if (x == 1 || x == 0) {
            return BigInteger.ONE;
        }
        if (arr[x] != BigInteger.ZERO) {
            return arr[x];
        }
        arr[x] = BigInteger.valueOf(x).multiply(fact(x - 1, arr));
        return arr[x];
    }
}