Correct Answer - `(16!)/((2!)^(8))`
The number of ways 16 constables can be divided into 8 bactes is `(16)!//8!(2!)^(8)`.
Now, the first batch may be assigned to patrol any of the 8 batches to patrol 8 villages is
`((16)!)/(8!(2!)^(8))(8!)=((16)!)/((2!)^(8))`