Determine the no. of arrangements in a circle tt are possible when the letters of the word EXCELLENT are used?

Answer 1

I reckon 30240 is right, provided you start always from the same position in the circle. If you regard EXCELLENT starting in position 1 as equivalent to EXCELLENT starting in position 2, then you would divide this by 9 to get 3360.

Answer 2

There are 9 letters so 9 places as illustrated below:

E X C E L L E N T
_ _ _ _ _ _ _ _ _

6 x 6 x 5 x 4 x 4 x 4 x 3 x 2 x 1 = 69,120 ways

because we have same letters like E and L... so for example the first letter will only have 6 ways, meaning the letter could start with E, X, C,L,N and T. then 2nd letter will still have 6 ways again because even if E was used in the first letter, we still have other E,... and third letter has 5 ways... This means that the 3rd letter could be C, E,L, N, T, and the fourth letter could be E, L N, T and so forth and so on.

Answer 3

Since it's a circle, and there is no "1st" letter, total combinations(before we start eliminating repeat letters) will be 8! rather than 9!

Now we have to eliminate combinations that have been counted more than once due to the fact that when identical letters are transposed, the arrangement remains the same, so...
2 L's and 3 E's.....8!/(2!*3!) =

8*7*5*4*3*1 = 3360

Answer 4

(Number of objects)!
(objects same)

9!
3!(E)2!(L)

= 30240

Sorry, thats for a straight line... i dont know.