Permutations And Combinations Question 376

Question: 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. Then the number of such arrangement is:

Options:

A) At least 500 but less than 750

B) At least 750 but less than 1000

C) At least 1000

D) Less than 500

Show Answer

Answer:

Correct Answer: C

Solution:

  • [c] 4 novels, out of 6 novels and 1 dictionary out of 3 can be selected in $ ^{6}C_4{{\times }^{3}}C_1 $ ways Then 4 novels with one dictionary in middle can be arranged in 4! Ways.
    $ \therefore $ Total ways of arrangement $ {{=}^{6}}C_4{{\times }^{3}}C_1\times 4!=1080 $