How many of
   each
 of these
  digits   
2's  3's  4's            Four-digit numbers                          Total  
----------------------------------------------------------------------------
 0    0   4     4444                                                    1
 0    1   3     3444, 4344, 4434, 4443                                  4
 0    2   2     3344, 3434, 3443, 4334, 4343, 4433                      6
 1    0   3     3233, 3323, 3332                                        3
 1    1   2     3244, 3424, 3442, 4234, 4243, 4324, 4342, 4423, 4432    9
 1    2   1     3234, 3243, 3324, 3342, 3423, 3432, 4233, 4323, 4332    9 
 2    0   2     4224, 4242, 4422                                        3
 2    1   1     3224, 3242, 3422, 4223, 4232, 4322                      6
 2    2   0     3223, 3232, 3322                                        3
-------------------------------------------------------------------------
                                                         Grand total = 44
                                                                       
Edwin