120
240
Algorithm is the only nine letter word.
The answer is 5!, 5 factorial. This equals 5 X 4 X 3 X 2 X 1, which is 120.
That's eight letters, so: 8! = 40320 different arrangements. n! means "factorial", and the expression expands to n*(n - 1)*(n - 2) ... * 2 * 1
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.
You have eight letters to work with, and can use any four of them, but only once per combination. That means that the total number of possible combinations you can make is: 8! / (8 - 4)! = 8! / 4! = 8 * 7 * 6 * 5 = 1680 So there are 1680 possible combinations.
720 (6 x 5 x 4 x 3 x 2)
There are 7!/(3!*2!) = 420 ways.7! for the seven letters in "success", butthere are 3 s which are indistinguishable, so divide by 3!there are 2 c which are indistinguishable, so divide by 2!
8 different 4-letter words can be formed from the letters of the word "Nation".
There are 5 ways to choose the first letter, 4 ways to pick the second letter, 3 ways to select the third, 2 options for the fourth letter leaving just one way to pick the final letter. The number of arrangements are thus 5 x 4 x 3 x 2 x 1 = 120
20! = 2432902008176640000
Words that can be made with the letters in 'gazebo' are:aageagobagbebegboabogegogabgazegogob