Rearrangements of LOLLIPOP with matching ends

Count the distinct arrangements of the eight letters of the word LOLLIPOP whose first and last letters are the same. (For example, LOLIPOPL qualifies.)

$300$. LOLLIPOP has three L, two O, two P and one I. With L at both ends the middle six letters (L, O, O, P, P, I) can be arranged in $\tfrac{6!}{2!\,2!}=180$ ways. With O at both ends, or P at both ends, there are $\tfrac{6!}{3!\,2!}=60$ ways each. I cannot be at both ends, so the total is $180+60+60=300$.