find the number of ways in which the letter of word CARACAS can be arranged so that the C do not appear together.

there are 7 letters with 3 A's and 2 C's
so arranging these letters in any way is 7!/(3!*2!) = (7*6*5*4*3!)/3!*2=420
now consider 2 C's as single unit as they appear together.
so now total number of lettes is 6(A,A,A,R,S,(CC))
now arranging this in any way is 6!/3!(because A appears 3 times)
6!/3!=120
120 times C appears together
so subtract 120 from 420 to get words in which C do not appear together.So the answer is 300.

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