In how many rearrangements of the word AMAZED, is the letter ‘E’ positioned in between the 2 ‘A’s (Not necessarily flanked)?

There are 6 boxes numbered 1, 2,…6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:

Company BELIANCE hosted a party for 8 members of Company AXIAL. In the party no member of AXIAL had interacted with more than three members of BELIANCE. Out of all the members of BELIANCE. Three members- each interacted with four members of AXIAL and the remaining members-each interacted with two members of AXIAL. The greatest possible number of members of company BELIANCE in the party is: