Answer Choice Randomization: Problem with randomized subset

You will probably have to do some javascript to achieve this.

Create a question with all 15 answers to use as a base.

In the javascript, make 3 random numbers to choose one from each group. Then hide the radio buttons for the non selected answers.

Note that this will not change the order of the buttons, it will only hide the buttons. If you want a random order, you will have to randomize the order of all 15 answers and then use the random number to select a pointer to the answer location.

Is your keyboard broken?

Seriously though, it is very easy to do this in Qualtrics. If you search the forum, there was a recent post on hiding the radio buttons. There are also many posts on randomizing.

Off the top of my head, here is a starting point:
var grp1 = [1, 4, 7, 10, 13]; // answer group 1 locations
var grp2 = [2, 5, 8, 11, 14];
var grp3 = [3, 6, 9, 12, 15];

var pick1 = Math.floor((Math.random() * 5)); // random number between 0 and 4
var pick2 = Math.floor((Math.random() * 5));
var pick3 = Math.floor((Math.random() * 5));

for (var i = 0; i < grp1.length; i++) {
if (i <> pick1) {
jQuery('input[type=radio]:nth-child(grp1[i])').hide();
}
}

repeat the above code for grp2/pick2 and grp3/pick3.

This should get you started.