Explanation:

- The average age of 45 students is 13 years, so their total age is 45 * 13 = 585 years.

- 15 new students join with an average age of 18 years, making their total age 15 * 18 = 270 years.

- Overall, there are now 45 + 15 = 60 students.

- The combined total age of all students is 585 + 270 = 855 years.

- The new average age is 855 / 60 = 14.25 years.

- Option 2: 14.25 years is the correct average age for all students.

Answer: Option 2: 14.25 years