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

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

2
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

$129729600 - 19958400 = 109771200 w a y s$

Hope this helps!

• 13 minutes ago
• 16 minutes ago
• 18 minutes ago
• 24 minutes ago
• 17 seconds ago
• 6 minutes ago
• 9 minutes ago
• 11 minutes ago
• 12 minutes ago
• 13 minutes ago
• 13 minutes ago
• 16 minutes ago
• 18 minutes ago
• 24 minutes ago