divide 11 members into four groups and select compulsory one member from each group then how many sum of all possible combinations we get by selecting any 7 members

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?

This problem involves dividing 11 members into 4 groups, selecting 1 compulsory member from each group, and calculating the total number of ways to select 7 members from the remaining. It explores combinatorics and the basic counting principle, suitable for Grades 10-12.

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