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 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
A. less than 500
B. at least 500 but less than 750
C. at least 750 but less than 1000
D. at least 1000

Answer 1

Out of 6 novels, 4 novels can be selected in `""^(6)C_(4)` ways and 1 dictionary can be chosen out of 3 dictionaries in `""^(3)C_(1)` ways. Since 1 dictionary is to be fixed in the middle and a pair of novels on its either side. This can be done in `""^(4)C_(2)xx2!xx2!` ways.
`:.` Required number of arrangements
`""^(6)C_(4)xx""^(3)C_(1)xx""^(4)C_(2)xx2!xx2!=1080`