Calculate the number of permutations of the word CALENDAR in which C and A are together but N and D are not.

This is what I did:

No. of possible permutations $\displaystyle \: = \frac {8!}{2!}\: =\: 20160.$

No. of permutations in which C and A are together $\displaystyle \: =\: 5! * \frac {3!}{2!}\: =\: 360.$

No. of permutations in which C and A are not together $\displaystyle = 20160 - 360 = 19800.$

No. of permutations in which N and D are together $\displaystyle \: = \frac {6!}{2!} * 2! = 720.$

No. of permutations in which N and D are not together $\displaystyle = 20160 - 720 = 19440.$

What next?

Thanks.

ILoveMaths07.