How many ways are there to arrange the letters in the word ALGORITHMS? Note, the letter arrangement does not have to spell a word in the dictionary, but the new word must contain all the letters and each letter can be used only once.

Question

09-07-2021
Computers and Technology

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How many ways are there to arrange the letters in the word ALGORITHMS? Note, the letter arrangement does not have to spell a word in the dictionary, but the new word must contain all the letters and each letter can be used only once.

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AlexTrusk AlexTrusk · Answer 1 · 2021-07-09T01:14:55+02:00

there are ten letters in the word, so for the first position we can choose out of 10 option.

no matter wich specific option we choose, we will have 9 letters left for the 2nd letter.

and 8 for the third place.

...

when we will have used up 9 of 10 letters, there will be only one option for the last place.

the number of possible decision-paths is therefore given by this expression:

10*9*8*7*6*5*4*3*2*1

wich is 3,628,800

there are quite a few ways to rearrange 10 letters

codiepienagoya codiepienagoya · Answer 2 · 2021-09-19T13:26:40+02:00

The sorting method which commands entries in a going to head predicated on each character without regard to space as well as punctuation, therefore there are 3628800 ways.

The word 'ALGORITHMS' has 10 letters.
There is no repeated letter so, the first Letter can hold 10 places if we start taking one letter at a time.
The second can then hold nine positions, the third can hold eight, and so on.

So, as [tex]\bold{ 10\times 9 \times 8.... \times 3 \times 2 \times 1 = 362,8800}[/tex] ways, we have such a total number of ways.

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