1,2,3,4,5,5

how many 4 digit numbers can i arrange the above 6 digits into?

I break it up into 3 cases:

case 1: 0 occurence of 5 : 1,2,3,4 = 4! ways = 24 ways

Case 2: 1 occurence of 5: 5xxx = 4C3 * 4! = 96 ways

Case 3 : 2 occurence of 5: 55xx = 4C2 * 4!/2! = 72 ways

Total = 192 ways.

Am I correct?