Answer:
144 seatings
Step-by-step explanation:
After Pierre sits, we can place Rosa either two seats from Pierre (that is, with one seat between them) or three seats from Pierre. We tackle these two cases separately:
Case 1: Rosa is two seats from Pierre. There are 2 such seats. For either of these, there are then four empty seats in a row, and one empty seat between Rosa and Pierre. Thomas can sit in either of the middle two of the four empty seats in a row. So, there are 2*2 = 4 ways to seat Rosa and Thomas in this case. There are then 4 seats left, which the others can take in 4! = 24 ways. So, there are 4*24 = 96 seatings in this case.
Case 2: Rosa is three seats from Pierre (that is, there are 2 seats between them). There are 2 such seats. Thomas can't sit in either of the 2 seats directly between them, but after Rosa sits, there are 3 empty seats in a row still, and Thomas can only sit in the middle seat of these three. Once again, there are 4 empty seats remaining, and the 4 remaining people can sit in them in 4!= 24 ways. So, we have 2* 24 = 48 seatings in this case.
Putting our two cases together gives a total of 96+48 = 144 seatings.