How many distinct arrangements can be made from the letters in the word "REARRANGE''?

Oofrence May 1, 2019

#1**0 **

Arrangements of how many letters in a "word"? 1-letter, 2-letters, 3-letters.........9-letters ??

Guest May 1, 2019

#3**-1 **

I can just explain this problem to you

We can first try to pick our firt letter to arrange it, we have 9 letters to put in our first position, 8 letters in the second, and so on so we get

9*8*7*6*5*4*3*2*1 For the total number of combinations

But, then we realize that we have repeating numbers,

Example: REARrANGE and REArRANGE are the exact same combinations(notice that the r's are counted as 1 combination becuase they are the same)

So from our 9!(9*8*7*6*5*4*3*2*1) we have to divide for our repeating numbers

we divide by 3! to make up for the r's and 2! to make up for the e's and another 2! to make up for the a's

Answer: 9!/3!*2!*2!

doorknoob May 2, 2019