colonia

Given length of character array (N), and number of each character appearing in this array (e.g. A is appearing nA times, B is appearing nB times etc, na+nB+..+nZ = N), what is the probability of character (say, _c) appearing m (m <= n_c) times in a row in this array? Let's say only characters are A and B. nA = 5 nB = 3 N = 8 and suppose m = 3 and _c = 'A' Situations of interest: AAA*****, *AAA****, **AAA*** etc. I assume the probability is: Do you agree?