Question

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

Answer 1

see a step process below;

Explanation:

Firstly you have to find the total arrangement which is;

`"ACCOMMODATION" = (13!)`

`"2C's"`

`"2M's"`

`"2A's"`

`"3O's"`

`(13!)/(2!×2!×2!×3!) =129729600 ways`

Then you have to find the arrangement if `"2Cs"` are adjacent;

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

`"1C's"`

`"2M's"`

`"2A's"`

`"3O's"`

`((13 - 1)!)/(3!×2!×2!)`

`(12!)/(3!×2!×2!) = 19958400 ways`

Then subtract both answers;

`129729600 - 19958400 = 109771200ways`

Hope this helps!