From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and…
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is
less than 500
at least 500 but less than 750
at least 750 but less than 1000
at least 1000
Solution
4 novels can be selected from 6 novels in ${ }^6 \mathrm{C}_4$ ways. 1 dictionary can be selected from 3 dictionaries in ${ }^3 \mathrm{C}_1$ ways. As the dictionary selected is fixed in the middle, the remaining 4 novels can be arranged in 4 ! ways.
$\therefore$ The required number of ways of arrangement $={ }^6 \mathrm{C}_4 \times{ }^3 \mathrm{C}_1 \times 4 !=1080$