Find All Combinations of array JavaScript

function combinations(str) {
    var fn = function(active, rest, a) {
        if (!active && !rest)
            return;
        if (!rest) {
            a.push(active);
        } else {
            fn(active + rest[0], rest.slice(1), a);
            fn(active, rest.slice(1), a);
        }
        return a;
    }
    return fn("", str, []);
}
var allArrays = [['a', 'b'], ['c'], ['d', 'e', 'f']]
function allPossibleCases(arr) {
  if (arr.length == 1) {
    return arr[0];
  } else {
    var result = [];
    var allCasesOfRest = allPossibleCases(arr.slice(1));  // recur with the rest of array
    for (var i = 0; i < allCasesOfRest.length; i++) {
      for (var j = 0; j < arr[0].length; j++) {
        result.push(arr[0][j] + allCasesOfRest[i]);
      }
    }
    return result;
  }
}
console.log( combinations("abcd") );
console.log( allPossibleCases(allArrays) );

O/P:
[object Array]: ["abcd", "abc", "abd", "ab", "acd", "ac", "ad", "a", "bcd", "bc", "bd", "b", "cd", "c", "d"]
[object Array]: ["acd", "bcd", "ace", "bce", "acf", "bcf"]