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From 6 different novels and 3 different ...

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 arrangements is

A

atleast 1000

B

less than 500

C

atleast 500 but less than 750

D

atleast 750 but less than 1000

Text Solution

Verified by Experts

The correct Answer is:
A
4 novels can be selected from 6 novels in `.^(6)C_(4)` ways. 1 dictionary can be selected from 3 dictionaries in `.^(3)C_(1)` ways. As the dictionary selected is fixed in the middle, the remaining 43 novels can be arragned in 4! Ways.
`therefore`The required number of ways of arrangement.
`=.^(6)C_(4)xx.^(3)C_(1)xx4! =1080`
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