Discussion Forum

From 6 different novels  and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf,

so that the dictionary is always in the middle. The number of such arrangement is  

Answer:

Explanation:

Given 6 different novels and 3 different dictionaries.

Number of ways of selecting 4 novels from 6 novel is $^{6}C_{4}=\frac{6!}{2!4!}=15$

  Number of ways of selecting 1 dictionary is from 3 dictionaries is $^{3}C_{1}=\frac{3!}{1!2!}=3$

$\therefore$     Total number of arrangement of 4 novels and 1 dictionary where dictionary is always in the middle is

                      $15\times 3\times 4!=45\times 24=1080$