There are 3 face cards per 4 suits, so there are 12 face cards in a deck.

The probability of getting one of the face cards on the first draw
is 12 ways out of 52.  So nds of all the times when we draw three cards,
the first one will be a face card.

Of the nds of the times when we draw a face card first, we will be
left with a deck of 51 cards, 11 of which are face cards.  Therefore
sts of the nds of the times when we draw a face card
first, we will draw a face card second sts of the times.  That's
*sts of the time when we draw three cards we will draw
the first two cards as face cards.

Of the *sts of the times when we draw a face card first
and a face card second, we will be left with a deck of 50 cards, 10 of which
are face cards.  Therefore ths of the *sts of
the times when we draw a face card the first and second times, we will draw a
face card third sts of the times.  That's **ths
of the time when we draw three cards we will draw all three of them as face
cards.

So the desired probability is **.

That reduces to ** or 

Now the 3 cancels into the 51, 17 times


  
   
So we end up with the probability

 or 

Edwin