Combinations and Permutations

Reviewing for finals and got this question wrong:

How many different permutations are there of the letters in the word LOLLIPOP

what I did was 8P8, how would you solve this?

nickar1172 said:

Reviewing for finals and got this question wrong:

How many different permutations are there of the letters in the word LOLLIPOP

what I did was 8P8, how would you solve this?

Click to expand...

You have to account for the fact that you have multiples of the same letters. So doing 8! as you did means that you are counting each of the L's, O's and P's as different letters, which they are not. You need to divide 8! by the product of the factorials of the number of repeating letters for each repeating letter. In this case there are 3 L's, 2 O's and 2 P's. Thus, the number of permutations would be:

\(\displaystyle \dfrac{8!}{3! \cdot 2! \cdot 2!}\)

thank you so much appreciated it