Question

How many permutations are there for the letters in the word LOLLIPOP?

Answer 1

distinguishable or all permutations?

Answer 2

all

Answer 3

\[\frac{8!}{3!2!2!}\]
The 8! ways of rearranging the letters in LOLLIPOP have to be dividedby 3!, 2! and 2! because having fixed the positions of the non-repeated letters, the L's may be arranged in 3! ways, the O's in 2! ways and the P's in 2! ways without making a different word.