Studugi question

[Phat Mack]

What percentage of seven-card hands contain a badugi? I've written a sim to montecarlo an answer, but wonder if anyone has calculated this, or can think of an elegant way to do so.

Whenever I try to enumerate hands that do, or do not, contain a bugugi, it seems I'm a few bricks short of a load.

Side questions: can anyone think of seven-card hands that contain N badugis, 0<N<4? N>8?