Question

What is the total number of different 10-letter arrangements that can be formed using the letters in the word ANTEBELLUM?

Answer 1

907,200 different 10-letter arrangements can be formed using the letters in the word ANTEBELLUM

Explanation:

Number of arrangments:

A word has n letters.

There are m repeating letters, each of them repeating times

So the number of distincts ways the letters can be permutated is:

`N_(A) = (n!)/(r_(1)! * r_(2)! * ... * r_(m))`

In this question:

ANTEBELLUM has 10 letters.

E and L each occur two times. So

`N = (10!)/(2!*2!) = 907200`

907,200 different 10-letter arrangements can be formed using the letters in the word ANTEBELLUM