on generating combinations among a variable list of lists

[Boris Dorestand]

Say we have [1,3,5,7], [2,3], [1,10].  I'd like to generate

  [1,2,1]
  [1,2,10]
  [1,3,1]
  [1,3,10]
  [3,2,1]
  [3,2,10]
  [3,3,1]
  [3,3,10]
  [5, ...]
  ... 
  [7,3,10]

The number of input lists is variable.  The example shows three lists,
but there could be only one or ten lists or any other number of lists.

I looked at itertools.  There doesn't seem to be any procedure ready for
this.  I might have to combine some of them but I'm not yet sure how.