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

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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!