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

Answer:

3628800

Step-by-step explanation:

There are 10 distinct letters in the word ALGORITHMS.

The total number of ways in which the letters can be arranged in a row is given by the permutations of a set with 10 elements.

P(10,10)=3628800

$P(10,10)=\frac{10!}{(10-10)!}$