Is it permissible to combine the Maghrib and Isha prayers, sufficing with three rak'ahs for Maghrib, then completing the remaining rak'ahs with the imam during the Isha prayer, due to joining the military college and arriving half an hour before the Isha adhan?

It is not permissible to combine two prayers without a valid excuse, and doing so is a major sin. What was mentioned is not a permissible excuse for combining prayers. A person can perform ablution and pray in the college or on the ground, for the earth is a mosque and purifying. If the Maghrib prayer is missed due to an excuse and the 'Isha prayer is caught, it is permissible for him to pray Maghrib behind the Imam who is praying 'Isha. This is the Madhhab (definition) of the Shafi'is and is the most preponderant opinion. It is better for him to sit during the third rak'ah and wait for the Imam to make the tasleem with him, or he can intend to separate from the Imam and make the tasleem. He can also, after concluding the Maghrib prayer, join the Imam in the 'Isha prayer.

He can also pray with the Imam with the intention of 'Isha, then pray Maghrib, as the order is waived due to the excuse. However, if combining prayers is permissible and he intended to combine them during the time of the first prayer, then the order must be observed (performing Maghrib before 'Isha). If he prays 'Isha then Maghrib, he must repeat 'Isha.