A student has to opt for 2 subjects out of 5 subjects for a course, namely Commerce, Economics, Statistics, Mathematics I and Mathematics II. Mathematics II can be offered only if Mathematics I is also opted. The number of different combinations of two subjects which can be opted is

The correct option is 7.

Let the 5 available subjects be represented as follows:
- Commerce (C)
- Economics (E)
- Statistics (S)
- Mathematics I (M1)
- Mathematics II (M2)

A student needs to choose exactly 2 subjects out of these 5, subject to the condition that Mathematics II (M2) can only be chosen if Mathematics I (M1) is also chosen.

We can analyze the valid combinations by dividing them into two cases based on whether Mathematics II (M2) is selected or not:

Case 1: Mathematics II (M2) is opted.
According to the given condition, if M2 is opted, then Mathematics I (M1) must also be opted. Since the student must choose exactly 2 subjects, choosing M2 forces the second subject to be M1. This gives us exactly 1 valid combination:
- {M1, M2}

Case 2: Mathematics II (M2) is NOT opted.
If M2 is not opted, the student must choose 2 subjects from the remaining 4 subjects (Commerce, Economics, Statistics, and Mathematics I). The number of ways to choose 2 subjects out of these 4 is given by the combination formula:

$$C_2^4=\frac{4\times 3}{2\times 1}=6$$

These 6 combinations are:
1. {C, E}
2. {C, S}
3. {C, M1}
4. {E, S}
5. {E, M1}
6. {S, M1}

Total Combinations:
Adding the combinations from both cases, we get:
Total combinations = 1 (from Case 1) + 6 (from Case 2) = 7.

Therefore, the number of different combinations of two subjects which can be opted is 7.