Question

Consider all of the distinguishable ways to arrange the letters in the word A P O C A L Y P S E in a row.
In total, there are 907200 such arrangements. Make sure you understand why before answering the following question.

Some of the 907200 arrangements will have the two As occuring consecutively, and will have the two Ps not occuring consecutively. An example of such an arrangement is P A A C O L Y P S E.
How many arrangements have both of these properties?