Simple but hard maths question

How many different ways can you arrange the letters of the word CHOCOLATE?

THere are 9 letters so you can start out by saying that you have

9 choices for the first letter, then 8, then 7, etc

9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 9!

But in those 9 letters there are two C's and two O's. The 9! value includes
words where the only difference the that the first and 2nd C swapped positions.
The same thing happens with the O's

You must divide by 2 to account for swapped C's and divide by 2 again to account for swapped O's.

So the final answer should be

9!/4 = 90720

Hi,

9 total letters, 2 Cs, 2 Os

. 9!
-------- = 90,720 distinguishable ways to arrange those letters <==ANSWER
2! 2!

I hope that helps!! :-)

Well the first letter can be 9 things. The second letter can only be 8 as the first one has gone. 3rd can only be 7 things and so on.

9! = 9*8*7*6*5*4*3*2*1

362880.