Since all the letters are different, the answer is 7! = 1 x 2 x 3 x 4 x 5 x 6 x 7.
If all the letters are unique in the set, there are 6 choices for the first letter, 5 for the second letter, 4 for the third letter, etc. This results in 6 X 5 X 4 X 3 X 2 = 720 arrangements. If some of the six letters are duplicated, there will be fewer distinct arrangements.
Assuming that you have to use all 4 of the letters with no repeats there are 4! or 4 factorial. Because you are asking how many ways can I arrange n objects if I use all n of them, the number of permutations is n!. To calculate factorials, you multiply the number by every integer before it until you reach 1. So 4! equals 4 X 3 X 2 X1 or 24. So there are 24 ways you can arrange the letters G,X,K, and T.
4 possibilities for the first letter to choose from S O C K.Then there are 3 letters to choose from for the second letter.Then there are 2 letters left to choose from for the third letter.Then there will be only 1 remaining letter left for the last of the four positions.So: We have 3 possibilities for the second letter for a total of 4 x 3 = 12 combinations.With 2 possibilities for the third letter we get 12 x 2 or 4 x 3 x 2 = 24 possibilities.Since there is only one letter left for the fourth position, it still is 4 x 3 x 2 x 1= 24 possibilities.In mathematics we abbreviate 4 x 3 x 2 x 1 to 4! (4 followed by an exclamation mark) and call it 4 factorial.
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720 ways
the answer is 4
Since all the letters are different, the answer is 7! = 1 x 2 x 3 x 4 x 5 x 6 x 7.
7 letters so factorial 7, ie 7 x 6 x 5 x 4 x 3 x 2 = 5040
The answer is 4! which is equal to 1 x 2 x 3 x 4.
Using all letters? You have seven different letters, so you can rearrange them in 7! (read: seven factorial) different ways, that is, 1 x 2 x 3 x 4 x 5 x 6 x 7.
The number of permutations of the letters of the word depends upon the number of letters in the word and the number of repeated letters. Since there are nine letters, if there were no repetitions, the number of ways to rearrange these letters would be 9! or 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1. But don't do the multiplication just yet. To account for the repeated letters, we need to divide by 3! (for the 3 Ns) by 2! (for the 2Es) and by another 2! (for the 2 Ss). This gives a final answer of 15,120 permutations of these letters.
Permutations of 7 letters = (7 x 6 x 5 x 4 x 3 x 2 x 1)Divide by 2 because swapping the two 'I's is indistinguishable.Divide by 2 because swapping the two 'L's is indistinguishable.Distinguishable permutations = (7 x 6 x 5 x 4 x 3 x 2) / 4 = 1,260
If all the letters are unique in the set, there are 6 choices for the first letter, 5 for the second letter, 4 for the third letter, etc. This results in 6 X 5 X 4 X 3 X 2 = 720 arrangements. If some of the six letters are duplicated, there will be fewer distinct arrangements.
A mathematical function known as factoring is applied. Written as n!, it is defined as n x n-1 x n-2 x . . . x 1 (where x means multiplied by) Example:Given thee letters A, B, C, D, and E, there are 5 choices for picking the first letter. Regardless of which letter is picked first, there are 4 choices for the second letter. Likewise there are 3 choices for the third, 2 for the fourth and 1 for the last. So, in this case, 5! = 5 x 4 x 3 x 2 x 1 = 120. There 120 different arrangements for 5 letters. This holds if all the letters are different. If any of the letters are the same, factor the number of different letters to come up with the answer. example: T, P, L, T, F would yield 4!, or 4 x 3 x 2 x 1 = or 24 distinct arrangements.
(5 x 4 x 3 x 2 x 1) = ( 5 ! ) = 120 ways.
ikln
Assuming that you have to use all 4 of the letters with no repeats there are 4! or 4 factorial. Because you are asking how many ways can I arrange n objects if I use all n of them, the number of permutations is n!. To calculate factorials, you multiply the number by every integer before it until you reach 1. So 4! equals 4 X 3 X 2 X1 or 24. So there are 24 ways you can arrange the letters G,X,K, and T.