It depends on the letters and also on the words that have been placed on the board.
720
64 different arrangements are possible.
181440
5! = 5x4x3x2x1 = 120
Permutations of 10 letters taken 3 a time = 10 x 9 x 8 = 720
Only 20.
Algorithm is the only nine letter word.
The number of different three letter arrangements that can be done from theletters in the word "mathematics"is; 11P3 =11!/(11-3)! =990
The letters of the word "art" can be ordered in 6 ways.
Only 20.
the arrangements occur. if there are two of the same letter then 12 all different letters then 24 three letters the same then 5 four letters the same then 1
If you pick from each of the possible letters at each stage, then there are 5 possible options for the first letter. Then there are 4 possible options for the second. Then there are 3 possible options for the 3rd and so on. This leaves us with 5x4x3x2 = 120 different arrangements. However, each arrangement has been counted twice, as it doesn't matter which way around the Os go. So to get the true answer, we need to divide by 2. 120/2 = 60, and therefore the number of different arrangements of the letters in the word COLOR is 60.
The number of 5 letter arrangements of the letters in the word DANNY is the same as the number of permutations of 5 things taken 5 at a time, which is 120. However, since the letter N is repeated once, the number of distinct permutations is one half of that, or 60.