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Combinations and Permutations

nickar1172

New member
Dec 11, 2013
20
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?
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
The number of ways to order or arrange $n$ objects is $n!$. So, we want to look at the number of ways to order 8 letters, however, there are 3 L's, 2 O's and 2 P's. Hence, you want to take the total number of ways to arrange 8 letters, and then account for the fact that some of them are identical. Can you state how many would be identical?

edit: I have removed the [SOLVED] label from the title so that our readers don't skip the thread thinking you have already found the solution yet.
 

nickar1172

New member
Dec 11, 2013
20
so it would be 8P8/2!3!2! = 1680?
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Yes, although I would simply write:

\(\displaystyle N=\frac{8!}{3!2!2!}=8\cdot7\cdot6\cdot5=1680\)