Assuming that by "arrange" you mean "order" (if you really mean "arrange", there are infinitely many possible ways to arrange even just two objects; you could separate them by 1 inch, or by 2 inches, or by 3.14159265... inches, and that's without even getting into left vs. right or above vs. below or at an angle of x degrees from horizontal) ...
You can choose any of the 6 to be first, any of the remaining 5 to be second, any of the remaining 4 to be third, and so on, down to the last one where you have no choice because it's the only one left.
That means there are 6x5x4x3x2(x1), or 6! = 720 possible orderings.
6 to the power of 6 so 6x6x6x6x6x6=46,656
6
6! = 720
If you have three DIFFERENT letters, you can arrange them in 3! = 1 x 2 x 3 = 6 different ways.
3 items (or people) can line up in 6 different sequences. 6 items (or people) can line up in 720 different sequences.
6
9×8×7×6×5=15,120
6 to the power of 6 so 6x6x6x6x6x6=46,656
6
6! = 720
In a line in 6! = 6*5*4*3*2*1 = 720 ways.
3*2*1 = 6 ways.
30 ways.
Since no letters are repeated in the word prime, you can arrange the letters in the word prime 5! ways, or 120 ways.
If you have three DIFFERENT letters, you can arrange them in 3! = 1 x 2 x 3 = 6 different ways.
The word "onomatopoeia" has 11 letters, with 6 vowels and 5 consonants. Therefore, there are 11!/(6!5!) = 33,120 ways to arrange the word "onomatopoeia".
6! = 6*5*4*3*2*1 = 720