Question

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

• 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

Answer: (D)

at least 1000

Answer 2

4 novels can be selected from 6 novels in $^6C_4$ ways. 1 dictionary can be selected from 3 dictionaries in $^3C_1$ ways. As the dictionary selected is fixed in the middle, the remaining 4 novels can be arranged in 4! ways. $?$ The required number of ways of arrangement $=^{6}C_{4}\times^{3}C_{1}\times4!=1080$