If number of ways of arranging letters aaaabbbbccdd in a line so that there should be at least one b in between two a’s is k, then the value of $\left|15000-k\right|$ is

Three b’s and four a’s can arrange abababa
Fourth ‘b’ can take 5 places, $\left\{\begin{array}{c}babababa\\ abbababa\\ ababbaba\\ abababba\\ abababab\end{array}\right.$ 
Take 8 place from 12 places and arrange letters in same order, cc dd can take remaining 4 place $\therefore {}^{12}{C}_8\times 5\times \frac{4!}{2!2!}$