I have an array of arrays
allArrays = [
    ['women', 'men'], // gender
    ['age 18-24', 'age 25-34', 'age 35-44', 'age 45 or over'] // age
]
Further, I want the order of these arrays to be randomized. I shuffle the arrays using Fisher-Yates Shuffle from this answer.
// shuffle array of arrays
function shuffle(array) {
  let currentIndex = array.length,  randomIndex;
  // While there remain elements to shuffle.
  while (currentIndex != 0) {
    // Pick a remaining element.
    randomIndex = Math.floor(Math.random() * currentIndex);
    currentIndex--;
    // And swap it with the current element.
    [array[currentIndex], array[randomIndex]] = [
      array[randomIndex], array[currentIndex]];
  }
  return array;
}
    
shuffle(allArrays)
Lastly, I want all the combinations of values. I combine the arrays using the recursive method this answer.
// get all combinations
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;
  }
}
let output = allPossibleCases(allArrays)
However because the order of the initial arrays is randomized the output is either arranged first by gender or first age. i.e., 'women, age 18-24', 'women, age 25-34', 'women age 35-44', ... or 'age 18-24, women', 'age 18-24, men', 'age 25-34, women', 'age 25-34, men', ...
The reordering of the string is the intended behavior. However, I am wondering if it is then possible to then arrange the output array so that the same gender/age are presented in the same position regardless of their initial shuffle. Ideally, the answer would work for n arrays where n > 1.
 
    