there are 20 teachers, of these are 8 maths teachers, 6 history teachers, 4 physics teachers and 2 geography teachers.
how many ways can the teachers be chosen if there are to be at least 2 maths teachers?
i know the correct way to do this is: total number of combinations - combinations if there are no maths teachers - combinations if there is 1 math teacher
or even: combination if there are 2 maths teachers + combinations if there are 3 maths teachers + combinations if there are 4 maths teachers
but, what's wrong with the following approach? it seems to make sense: first, choose 2 from the 8 maths teachers, and then choose the other 2 from the remaining 18 teachers
this gives a completely dfiferent answer
(Edited something i completely mistakenly typed in)