Permutation-Combination
Aptitude

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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

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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:

$=120-48$

$= \textbf{72}$


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