To solve this problem, let's define the sets:

• Let $S$ represent the set of students selected for sports.
• Let $N$ represent the set of students selected for NCC.

We know the following:

1. Total number of students in the group = 15.
2. Number of students selected for only sports = 8.
3. Number of students selected for both sports and NCC = 4.

We are tasked with finding the number of students selected for only NCC.

Step-by-step solution:

• The total number of students selected for sports, which includes both students selected for only sports and those selected for both sports and NCC, is $|S| = 8 + 4 = 12$.
• Let $x$ represent the number of students selected for only NCC.
• The total number of students selected for only sports, both sports and NCC, and only NCC must add up to 15, the total number of students in the group.

Thus, we can form the equation:

$8 \text{ (only sports)} + 4 \text{ (both sports and NCC)} + x \text{ (only NCC)} = 15$

Simplifying this:

$12 + x = 15$

$x = 15 - 12 = 3$

Conclusion:

The number of students selected for only NCC is 3.

Would you like more details or have any questions?

Here are 5 related questions for practice:

1. What if 6 students were selected for both sports and NCC, how would that affect the result?
2. What if the total number of students was 20 instead of 15?
3. Can you generalize this problem for any number of students in sports and NCC?
4. How many students are not selected for any activity?
5. What would happen if no student was selected for both sports and NCC?

Tip: Always double-check if the numbers in set problems include overlaps like "both" categories.