No Problem.

If both groups are singing only notes in the major scale - easy - a major chord.

If one group sings a note from the minor scale, as long as the other group is only singing (in the major scale) notes that do not cause a dissonance, then you will hear a minor chord.

You see, the trick depends on the fact that most of the notes overlap between the two scales - especially if you use the Relative Minor to the Major - eg C Major & A Minor..

I'm sure someone else could describe it with a lot more words though...