12! = 479001600
/pre>
What is the probability that all the Mathematics books will not be arranged together?
We will get the probability of the complement event -- the probability
of one of these 9 ways occurring where the math books are all together.

MMMMEEEEEEEE, EMMMMEEEEEEE, EEMMMMEEEEEE, EEEMMMMEEEEE, EEEEMMMMEEEE,
EEEEEMMMMEEE, EEEEEEMMMMEE, EEEEEEEMMMME, EEEEEEEEMMMM.

In each of those 9 ways the Math books can be arranged 4! ways and the
English books can be arranged 8! ways. The probability that they will be
together is   =  =  = 0.0181818182.

So the probability that they will NOT all be together is 1- =  = .9818181818.

Edwin
 

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