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 (1) less than 500 (2) at least 500 but less than 750 (3) at least 750 but less than 1000 (4) at least 1000

Options

A. atleast 1000
B. less than 500
C. atleast 500 but less than 750
D. atleast 750 but less than 1000

Answer

A

Explanation

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`