To find: number of words such that C and T are never together
Number of words where C and T are never the together = Total numbers of words - Number of words where C and T are together
Total number of words = \(\frac{7!}{2!}\) = 2520
Let C and T be denoted by a single letter Z
New word is APAINZ
This can be permuted in \(\frac{6!}{2!}\) = 360 ways
Z can be permuted among itself in 2 ways
⇒ Number of words where C and T are together = 360 × 2 = 720
⇒ Number of words where C and T are never together = 2520 - 720 = 1800
There are 1800 words where C and T are never together
