Number of arrangements with no consecutive letter the same - without using Jair Taylor's formula

Question

This is continuation to my question here. I find that complexity of this problem increases as the number of repeating letters increases. For example, consider the below problem.

How many arrangements of the letters in the word PQRDDDEEEEFFFFF have no consecutive letter the same?

Note:I have gone through all similar problems here and well aware of the common methods used. However, I could not apply any of the methods learned for the above problem. Please help, how to solve the above problem without using Jair Taylor's formula.

Answer 1

After lot of search, I came across this tool in careerbless.com and using that I solved both the problems. Posting it here for other readers benefit.

Question $1.$

Number of arrangements using the word 'PQRDDDEEEEFFFFF' having no consecutive letters the same

Answer Generated Using The Tool is $3659160$ with the following explanation
(see question no.$23$ in the generated question list after entering the word 'PQRDDDEEEEFFFFF')

Question $2.$

Number of arrangements using the word 'KOMBINATOORIKA' having no consecutive letters the same

Answer Generated Using The Tool is $710579520$
(see question no.$24$ in the generated question list after entering the word 'KOMBINATOORIKA') (explanation is very lengthy as the previous one and not posting it here)