Question

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.

Hint: Start with shorter words (e.g ALG or ALGO) and see if a pattern emerges with the number of possible arrangements.

Answer 1

The word 'ALGORITHMS' has 10 letters.

There is no repeated letter.

Then $10!=10(8)(8)...(1)=3628800$

There are 3628800 ways to arrange the letters in the word ALGORITHMS.