Determine the number of permutations of the multiset T = {3*a, 4*b, 2*c} where, for each type of letter, the letters of the same type do not all appear consecutively. (Thus aabbacbcb is allowed, but accbababb is not.)

I know the inclusion-exclusion principle is ideal for this situation, but I don't know how to do this..

Thanks in advance!!