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.