What is the number of ways letters in the word KOMBINATOORIKA can be rearranged, such that no two consecutive letters are the same? (the correct answer should be $710579520$, not $100\%$ sure though)
answer provided in www.algebra.com is $498960000$ , screenshot is given below
Here is the output of a tool given by careerbless.com [enter the word 'KOMBINATOORIKA', click on generate and answer to the 24th question generated] which gives the final answer as $710579520$
I feel answer is $498960000$ and not $710579520$. For small strings, I had a program using which I was verifying the right answer. But in this case I cannot do it as it is a large string. Could you please help me to find which is the right answer and reason for one answer being wrong.