MySQL 8.0

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CREATE TABLE WorkGroups ( ID varchar(64), GroupName varchar(64), MaxMembers int );

CREATE TABLE WorkEmployees ( ID varchar(64), EmployeeName varchar(64), WorkGroupFK varchar(64) );

INSERT INTO WorkGroups VALUES(1,'test1',2),(2,'test1',3),(3,'test1',2)
INSERT INTO WorkEmployees VALUES (1,'emp1', NULL),(2,'emp2', NULL),(3,'emp3', NULL),(4,'emp4', NULL)
,(5,'emp5', NULL),(6,'emp6', NULL),(7,'emp7', NULL)
  UPDATE WorkEmployees
     SET WorkGroupFK = ( SELECT WorkGroups.ID
                           FROM WorkGroups
                          WHERE ( SELECT COUNT(*) 
                                    FROM (SELECT * FROM WorkEmployees) WorkEmployees2
                                   WHERE WorkEmployees2.WorkGroupFK = WorkGroups.ID ) 
                                         < WorkGroups.MaxMembers 
						ORDER BY RAND()
                        LIMIT 1) /* max capacity */
   WHERE WorkEmployees.WorkGroupFK IS NULL /* employee not yet assigned */ 
   ;
SELECT * FROM WorkEmployees


ID
EmployeeName
WorkGroupFK


1
emp1
2

2
emp2
2

3
emp3
3

4
emp4
3

5
emp5
1

6
emp6
3

7
emp7
2