Answer
The possible schedules are represented below using a tree diagram.
There are $2\times15=30$ different schedules.
Work Step by Step
Denote the 2 English classes as E1, E2,
the 3 mathematics classes as M1, M2, M3,
the 5 electives as T1, T2, T3, T4, T5,
and the same first-year seminar as S.
