Question

How man ways may the letters in lollipop be arranged

Answer 1

8

Answer 2

we can use the multinomial factor theorem

Answer 3

I will do a different example, and you can get the idea.
How many ways to rearrange MISSISSIPPI ?

there are 11 letters in all
so

11! , but we are overcounting. we have to divide by the number of ways we are overcounting

Answer 4

so it helps if you consider
SSSS IIII PP M

if we use 11! we are treat it like s1 s2 s3 s4 i1 i2 i3 i4 p1 p2 m (but they are indistinguishable).
so we need to divide by 4! , 4! , 2! , to deal with the overcounting