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

Question

3097 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-09T15:56:04

see a step process below;

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!