Question

From six different novels and three different dictionaries, four novels and one 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

• 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

The correct option is D at least 1000.

Four novels can be selected from six novels in ${}^6{C}_4$ ways. One dictionary can be selected from three dictionaries in ${}^3{C}_1$ ways. As the dictionary selected is fixed in the middle, the remaining four novels can be arranged in 4 ! ways.
Hence, the required number of ways of arrangement is ${}^6{C}_4{\times }^3{C}_1\times 4!=1080.$