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

Answer 1

novel=`.^6C_4`
dietenary= `.^3C_1`
total choose=`.^6C_4 .^3C_1`
`- - D - - = 4!`
total arrangement=`.^6C_4 .^3C_1* 4!`
`= (6!)/(4!2!)*3*4!`
`= 1080`
option 4 is correct