SOLUTION: find the number of permutations of letters of CALENDAR in which C and A are together but N and D are not?

Question 266416: find the number of permutations of letters of CALENDAR in which C and A are together but N and D are not?
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
find the number of permutations of letters of CALENDAR in which C and A are together but N and D are not?


That's 

the number of ways C&A are together 

minus

the number or ways C&A are together and N&D are together

So:

N(C&A together) =  number of permutations of these 7 things:

{CA,L,E,N,D,A,R), which is 7! 

plus the number of permutations of these 7 things:

{AC,L,E,N,D,A,R), which is also 7!

So that's 2*7!

----------

N(C&A together and N&D together) = 

the number of permutations of these 6 things:

{CA,L,E,ND,A,R} which is 6!

plus 

the number of permutations of these 6 things:

{CA,L,E,DN,A,R} which is 6!

plus

the number of permutations of these 6 things:

{AC,L,E,ND,A,R} which is 6!

plus

the number of permutations of these 6 things:

{AC,L,E,DN,A,R} which is 6!

which is 4*6!

----------------------

Therefore the desired number is 

2*7! - 4*6! = 2*5040 - 4*720 = 10080 - 2880 = 7200 

Edwin

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