There are 6 different novels and 3 different poetry books on a table. If 4 novels and 1 poetry book are to…
There are 6 different novels and 3 different poetry books on a table. If 4 novels and 1 poetry book are to be selected and arranged in a row on a shelf such that the poetry book is always in the middle, then the number of such possible arrangements is
270
180
540
1080
Solution
Number of ways 4 novels can be selected out of 6 novels $-{ }^6 C_4$ and number of ways 1 poctry book can be selected out of $3={ }^3 C_1$
Number of arrangements can be made with 4 novels and 1 poetry book keeping poetry book in the middle $=4$ !
$\therefore$ Total required arrangements $={ }^6 C_4 \times{ }^3 C_1 \times 4!=1080$.