JEE Main 2018 (Offline)Question 1
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. The number of such arrangements is:
Permutation and Combination
Solution
Choose ${}^6C_4\cdot{}^3C_1=45$, fix the dictionary in the middle and arrange the $4$ novels in $4!=24$ ways: $45\cdot24=1080$, which is at least $1000$.