language agnostic - Algorithm to calculate combinations without duplicates -

i have following problem:

calculate combination of 3 digits number consisting of 0-9, , no duplicate allowed.

as far know, combinations don't care ordering, 123 equal 312 , number of possible combinations should

( 10 ) = 120 combinations (  3 ) 

that said: know how calculate permutations (via backtracking) don't know how calculate combinations.

any hint?

finding comnbination done via backtracking. @ each step - "guess" if should or should not add current candidate element, , recurse on decision. (and repeat both "include" , "exclude" decisions).

here jave code:

public static int getcombinations(int[] arr, int maxsize) {      return getcombinations(arr, maxsize, 0, new stack<integer>()); } private static int getcombinations(int[] arr, int maxsize, int i, stack<integer> currentsol) {      if (maxsize == 0) {         system.out.println(currentsol);         return 1;     }     if (i >= arr.length) return 0;     //"guess" include:     currentsol.add(arr[i]);     int x = getcombinations(arr, maxsize-1, i+1, currentsol);     //clean up:     currentsol.pop();     x += getcombinations(arr, maxsize, i+1, currentsol);     return x; } 

you can run following demo:

public static void main(string args[]) {     int[] data = {0,1,2,3,4,5,6,7,8,9};     int x = getcombinations(data, 3);     system.out.println("number of combinations generated: " + x); } 

and series of combinations, , @ number of combinations printed (unsurprisingly, 120)