I found these two sentences in RosettaStone
kochira no sanbanme no seki desu
kanojo wa hachiban no seki ni suwatte imasu
Why is the first one not "sanban" and the second one not "hachibanme"?
You can think of it like
◯-ban ↔ no. ◯
◯-banme ↔ ◯st,nd,rd,th
so
sanbanme no seki = the third seat
hachiban no seki = seat no. 8
There are a few related questions, but they usually use hiragana and kanji: