a) There are 12 letters, and if these were all unique, there would be 12! unique ways to arrange them.   However, we must divide out the duplicate (non-distinct) arrangements.   For this, we note there are 2 A's, 2 R's, 2 N's, and 2 E's, each of which contributes 2! non-distinct arrangements:



    Number of unique arrangements =   = 29937600





Part (b) can be done similarly.  Since the arrangements begin with EE, that effectively leaves 10 letters to arrange, and you'll need to remove duplicates in a similar way as in part (a).  It is as if the E's are removed and you repeat part (a) without the E's. 



Hint:  the answer will be  10! / (something) 

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
 .





                To tutor @math_helper







                Dear tutor @math_helper







If you open your post with  < pre >,





then you should  CLOSE  the post with the symbols  < / pre >,  for accuracy.







In addition to accuracy, it makes an influence at the appearance of your post.



Suddenly, you will discover that the appearance becomes to be manageable (!), in a way as you expect it (!!)







Best regards

@ikleyn







 

RELATED QUESTIONS

in how many ways can the letters of the word PERIMETER be arranged? also arrange four... (answered by stanbon)

In how many different ways can the letters of the word CALCULUS be arranged? How many of... (answered by Edwin McCravy)

In how many different ways can the letters of the word CIVILIZATION be... (answered by sudhanshu_kmr)

In how many different ways can the letters of the word BERIBERI be... (answered by edjones)

(a) How many different ways can 2 letters from the word SELECT be arranged?
(b) How many  (answered by ikleyn,math_tutor2020)

In how many different ways can any 4 of the letters in the following word be arranged?

 (answered by brucewill)

in how many different ways can the letters of word "MATHEMATICS" 
be arranged so that... (answered by Edwin McCravy)

in how many ways can the letters of the word TIMBERWOLVES be arranged using only 4... (answered by )