How many different ways are there of arranging the letters in the word ACCOMMODATION if no two Cs may be together?
1 Answer
Sep 19, 2016
Explanation:
ACCOMMODATION has
#3# O's#2# each of A, C, M#1# each of D, T, I, N
If the letters were all different, then there would be
As it is, the total number of distinct ways of arranging all
#(13!)/(3!2!2!2!) = 6227020800/(6*2*2*2) = 6227020800/48 = 129729600#
If the two letter C's are adjacent, then it is as if we are arranging
#3# O's#2# each of A, M#1# each of D, T, I, N and CC
The number of ways that we can do that is:
#(12!)/(3!2!2!) = 479001600/(6*2*2) = 479001600/24 = 19958400#
So the total number of ways of arranging the letters of ACCOMMODATION with no
#129729600 - 19958400 = 109771200#