Committee Combination


I have used the below formulation of the problem. Kindly let me know whether I am correct or wrong.

Q. "A condominium management committee has 11 members and wishes to divide into three committees with everyone serving on at least one committee, and no one serving on more than one committee. The committees are “Facilities”, which is to have 3 members; “Services” which is to have 5 members; and “Entertainment”, which is to have 3 members. How many ways can the 11 be split into these committees?"


11 C 3 + 11 C 5 + 11 C 3 = 792