(a) There can be two types of numbers :

$(i)$ Any one of the digits $1, 2, 3, 4$ repeats thrice and the remaining digits only once $i.e.$ of the type $1, 2, 3, 4, 4, 4$ etc.

$(ii)$ Any two of the digits $1, 2, 3, 4$ repeat twice and the remaining two only once $i.e.$ of the type $1, 2, 3, 3, 4, 4$ etc.

Now number of numbers of the $(i)$ type

$ = \frac{{6\;!}}{{3\;!}}{ \times ^4}{C_1} = 480$

Number of numbers of the $(ii)$ type

$ = \frac{{6\;!}}{{2\;!\;2\;!}}{ \times ^4}{C_2} = 1080$

Therefore the required number of numbers

$ = 480 + 1080 = 1560$.