# How many different ways are there of arranging the letters in the word ACCOMMODATION if no two Cs may be together?

Feb 9, 2018

see a step process below;

#### Explanation:

Firstly you have to find the total arrangement which is;

"ACCOMMODATION" = (13!)

$\text{2C's}$

$\text{2M's}$

$\text{2A's}$

$\text{3O's}$

(13!)/(2!×2!×2!×3!) =129729600 ways

Then you have to find the arrangement if $\text{2Cs}$ are adjacent;

"ACOMMODATION" = ((13 - 1)! = 12!)

$\text{1C's}$

$\text{2M's}$

$\text{2A's}$

$\text{3O's}$

((13 - 1)!)/(3!×2!×2!)

(12!)/(3!×2!×2!) = 19958400 ways

$129729600 - 19958400 = 109771200 w a y s$