How to make random groups with each number is used equal times

[jhendo14]

I am trying to figure out the following problem...I have a list of 12 numbers (1-12) and I am looking to make a random selection of 6 groups of 4 and each number being selected no more than 3 times in the group.

I could do this manually, but I have to apply it to a list of 240 with larger sets of random groups, so I will apply the logic to this question to my data set.

 

[sijpie]

just to clarify:
is it:

1. a number can appear more than once in a group, but not more than three times in one group, or
2. a number can appear only once in a group, but in no more than three groups

please let me know