arr = [
        ['a', 'b'],
        ['1', '2', '3'],
        ['x', 'y'],
    ]
    results = [];
    result = [];
    doExchange(arr, 0);
    function doExchange(arr, index){
        for (var i = 0; i<arr[index].length; i++) {
            result[index] = arr[index][i];
            if (index != arr.length - 1) {
                doExchange(arr, index + 1)
            } else {
                results.push(result.join(','))
            }
        }
    }

    console.log( results);//

results.png