The problem requires us to divide 11 members into 4 groups, then select 1 compulsory member from each group. After this, we need to calculate how many different combinations of 7 members can be selected from the remaining members.

Step-by-Step Breakdown:

1. Dividing 11 members into 4 groups: Let the groups have the following sizes:

   • Group 1: $a_1$
   • Group 2: $a_2$
   • Group 3: $a_3$
   • Group 4: $a_4$

   Since we have 11 members, we must ensure the group sizes satisfy: $a_1 + a_2 + a_3 + a_4 = 11$

2. Selecting 1 compulsory member from each group: We are asked to choose 1 member from each group. This will account for 4 members in total, leaving $11 - 4 = 7$ members to choose from the remaining.

3. Selecting 7 members from the remaining after compulsory selections: Now, we need to calculate the number of ways we can select 7 members from the remaining members. These remaining members would belong to the groups after the 1 compulsory member has been selected from each group.

   To select 7 members, the number of ways depends on how many members are left in each group. Assuming the remaining members form a new set after compulsory selection, the number of possible combinations can be calculated by considering the different sizes of remaining groups.

Would you like a further breakdown of the combinations based on specific group sizes?