(a) In how many ways can the seven (identical) horses on a carousel be painted with black, brown, and white paint in such a way that there are three black, two brown, and two white horses?
(b) In how many ways would there be equal numbers of black and brown horses?
(c) Give a combinatorial argument to verify that for all n ∈ Z+, n7 + 6n is divisible by 7.