Question 607151

There are {{{10!}}} unique arrangements of {{{10}}} different objects (the objects in this case are letters). 

But since we have {{{3}}} {{{A}}}'s, {{{2}}}{{{ P}}}'s and {{{2}}}{{{ E}}}'s, we must divide by the number of ways those can be rearranged creating indistinguishable combinations. 

That is {{{3! *2!* 2!}}}, meaning the answer is:

{{{10! / (3!* 2!* 2!) = 3628800/24=151200}}}