There were seven elective courses $\text{E1}$ to $\text{E7}$ running in a specific term in a college. Each of the $300$ students enrolled had chosen just one elective from among these seven. However, before the start of the term, $\text{E7}$ was withdrawn as the instructor concerned had left the college. The students who had opted for $\text{E7}$ were allowed to join any of the remaining electives. Also, the students who had chosen other electives were given one chance to change their choice. The table below captures the movement of the students from one elective to another during this process. Movement from one elective to the same elective simply means no movement. Some numbers in the table got accidentally erased; however, it is known that these were either $0$ or $1$.
|
Form Elective
|
To Elective |
| |
E1 |
E2 |
E3 |
E4 |
E5 |
E6 |
| E1 |
9 |
5 |
10 |
1 |
4 |
2 |
| E2 |
|
34 |
8 |
|
2 |
2 |
| E3 |
2 |
6 |
25 |
|
|
2 |
| E4 |
|
3 |
2 |
14 |
|
4 |
| E5 |
|
5 |
|
|
30 |
|
| E6 |
|
7 |
3 |
|
2 |
9 |
| E7 |
4 |
16 |
30 |
5 |
5 |
41 |
Further, the following are known:
- Before the change process there were $6$ more students in $\text{E1}$ than in $\text{E4}$, but after the reshuffle, the number of students in $\text{E4}$ was $3$ more than that in $\text{E1}$.
- The number of students in $\text{E2}$ increased by $30$ after the change process.
- Before the change process, $\text{E4}$ had $2$ more students than $\text{E6}$, while $\text{E2}$ had $10$ more students than $\text{E3}$.
How many elective courses among $\text{E1}$ to $\text{E6}$ had a decrease in their enrollments after the change process?
- $4$
- $1$
- $2$
- $3$