Unduplicated List of Trios

Greetings fellow Excelers and I hope everyone is safe and healthy.

The goal here is to establish a set of multiple groups of three random names from a list of people. Each group must be unique and subsequent sets of groups thereafter must also be unique such that no group is ever repeated.

Assume Column A has 150 unique names.

Round One of Trios:
Group 1: Random Person 1, Random Person 2, Random Person 3
Group 2: Different Random Person 1, Different Random Person 2, Different Random Person 3
Group 3: Different Random Person 1, Different Random Person 2, Different Random Person 3

This round of groups are unique and unduplicated.

Round Two of Trios:
All groups of three need to be non-duplicative trios of Round One.

Sample attachment provided.

Any guidance would be most appreciated.

I'm not sure I understand, but it feels like a "shuffle" kind of problem.

1) Enter =RAND() into B2 and copy down to B151.
2) Select B2:B151 and copy-> Paste Special -> Values (so the random numbers don't change).
3) Sort columns A and B according to column B.

A2:A4 is now one random group of 3, A5:A7 is a second, and so on down the column. Each person appears once through the entire list.

Is that what you are trying to do?