# Moderate Permutation-Combination Solved QuestionAptitude Discussion

 Q. There are five comics numbered from 1 to 5. In how many ways can they be arranged, so that part-1 and part-3 are never together?
 ✖ A. 48 ✔ B. 72 ✖ C. 120 ✖ D. 210

Solution:
Option(B) is correct

The total number of ways in which 5 part can be arranged $= 5! =120$.

The total number of ways in which part-1 and part-3 are always together:

$= 4!×2!$

$= 48$

Therefore, the total number of arrangements, in which they are not together is:

$=120-48$

$= \textbf{72}$