Initially, each boy has 10 cards:

A: 10 cards B: 10 cards C: 10 cards D: 10 cards E: 10 cards F: 10 cards

Now, let's follow the exchanges:

F borrows 2 cards from A:

A: $10 - 2 = 8$ cards F: $10 + 2 = 12$ cards F gives 5 cards to C:

F: $12 - 5 = 7$ cards C: $10 + 5 = 15$ cards C gives 3 cards to B:

C: $15 - 3 = 12$ cards B: $10 + 3 = 13$ cards B gives 6 cards to D:

B: $13 - 6 = 7$ cards D: $10 + 6 = 16$ cards D gives 1 card to E:

D: $16 - 1 = 15$ cards E: $10 + 1 = 11$ cards

Now let's check the number of cards possessed by D and E:

D: 15 cards E: 11 cards Total = $15 + 11 = 26$ cards

Now, let's check the total number of cards for different groups:

A, B, and C:

A: 8 cards B: 7 cards C: 12 cards Total = $8 + 7 + 12 = 27$ cards B, C, and F:

B: 7 cards C: 12 cards F: 7 cards Total = $7 + 12 + 7 = 26$ cards A, B, and F:

A: 8 cards B: 7 cards F: 7 cards Total = $8 + 7 + 7 = 22$ cards A, C, and F:

A: 8 cards C: 12 cards F: 7 cards Total = $8 + 12 + 7 = 27$ cards The correct answer is: B. B, C and F