1)

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  


A) atleast 1000

B) less than 500

C) atleast 500 but less than 750

D) atleast 750 but less than 1000

Answer:

Option A

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

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