The total number of groups is 47.
The number of groups of three or more distinct numbers that can be chosen from 1, 2, 3, 4, 5, 6, 7 and 8 so that the groups always include 3 and 5, while 7 and 8 are never included together is 47.
We can choose 2 out of the remaining 6 in 6C2 = 15 ways. We remove 1 case where 7 and 8 are together to get 14 ways.
But we must remove the case where neither of the 4 numbers are placed because the number becomes a two-digit number. Hence 16 - 1 = 15 cases.
Therefore, the total number of groups is 15 + 32 = 47.