Question

How many different ways can the first 10 letters of the alphabet be arranged?

Answer 1

There are 3,628,800 ways to arrange those letters. See explanation for details.

Explanation:

We can solve this task in 2 ways:

• We can choose 1 letter at a time and see in how many ways can it be chosen.

First letter can be chosen from all `10`, next from `9`, third from `8` and so on until you have only one letter left.
So the number of ways to arrange the letters can be calculated as:

`n=10xx9xx8xx7xx6xx5xx4xx3xx2xx1=3,628,800`

• Other way can be to treat the possible arrangement as a permutation of `10` element set. The number of permutations can be calculated as:

`P_n=n! =1xx2xx...xxn`