Question 459764
You should note that the P's are indistinguishable if you are looking for distinct arrangements.


If the 3 P's must be together, we can treat the three P's as one giant letter. Then, there are four "letters" to be arranged, creating 4P4 = 24 arrangements.


If the arrangement must begin and end with a P, then we have the letters E, I, P, S, and U to arrange in the center. Here, there are 5P5 = 120 arrangements.


Note that I did not treat the P's as being distinct.