The question is
I have a class of 10 students. The class consists of 4 statistics majors, 3 philosophy majors, and 3 sociology majors.
I choose three students at random, without replacement. (Order doesn’t matter.)
Let event A be "All three students I choose are statistics majors."
Let event B be "At least one student I choose is a philosophy major."
For P(A) I did $$4/10 \cdot 3/9 \cdot 2/8 = .033$$
For P(B) I thought it would be $$(7!\cdot 3!)/(10!) = .833$$ But that is not correct. I am a little confused on where I am going wrong, I thought it would be number of events that satisfy B/number of equally likely events some help in the right direction is all im asking for, thank you in advance.