当a great many（后接可数名词复数）后的名词是特指,即有the,these,those,my等限定词时,就用of.
1,A good /great many of the students have finished their homework.
这些学生中的很多人已经完成了功课.（强调完成功课的学生）
2,A great/good many students are playing basketball on the playground.
许多学生在操场上打篮球.（泛指打球的学生）
我觉得是你在迷惑这两个短语的用法,所以这样来回答你,