pulling a random item from multiple arrays

I have 12 arrays named f1 to f12 each with five items. I want to randomly pull one item from each array and push these into the new array sm1.

var sm1 = [];

for (var i=1; i<=12; i++) {
    randomPrompt = Math.floor((Math.random() * 5));
    sm1.push("f"+i[randomPrompt]);
}

However, this returns a random index of "f"+i instead of it indexing f1, f2, f3, f4, etc.