Recursive program to find the number of ways a particular amount can be obtained using a given set of Currency values.

public class Coins {
 private static int count = 0;
 public static void main(String[] args) {
  int[][] currencyList = {{5,10,20},{0,0,0}};
  //The first row contains the list of the currency values available.
  //The second row contains the frequency of each currency value.
  //The number of columns in both the rows should be the same.
  //Else an index-out-of-bounds exception will happen.
  int sum=0;
  int amount = 20;
  int index=0;
  computeCombinations(currencyList, sum, amount, index);
  System.out.println("Total possible combinations: "+ Coins.count);
 }

 public static void computeCombinations(int[][] currencyList, int sum, int amount, int index) {
  if(index >= currencyList[0].length) {
   return;
  }
  else {
   for(int i=0; i<=(amount/currencyList[0][index]);i++) {
    currencyList[1][index]=i;
    sum+=currencyList[0][index]*currencyList[1][index];
    if(sum == amount) {
     count++;
     for(int j=0;j <=index; j++) {
                                                if(currencyList[1][j] != 0) {
                                                        System.out.print(currencyList[0][j] + "-->" + currencyList[1][j] + " ");
      }
     }
     System.out.println();
    }
    else {
     computeCombinations(currencyList, sum, amount, index + 1);
     sum-=currencyList[0][index]*currencyList[1][index];
    }
   }
  }
 }
}
Output:
20-->1 
10-->2 
5-->2 10-->1 
5-->4 
Total possible combinations: 4