This is what I think so far, is that correct? Please help.

Design a non-deterministic automaton and regular expression over the alphabet {a, b, c} that accept all and only those strings that contain exactly three a's, three b's, or three c's, not necessarily consecutively. Strings in this language include:{aaa, abaab, abbcccccccccccbaaa,cbccbbbbbbb,...} . Also, design a regular expression for this language.

As a regular expression I think it would be like [bc]*a[bc]*a[bc]*a[bc]* but I'm not sure.

For an NDA, it would be like :