Select the correct combination of mathematical signs to sequentially replace the $\ast$ signs and balance the given equation.
$$16\ast 17\ast 14\ast 2\ast 3\ast 251$$

Let's test the sign combinations using the BODMAS rule to balance the equation:
* Option A: $\times ,-,÷,\times ,=$
Substitute the signs into the equation:

$$16\times 17-14÷2\times 3=251$$

Applying the BODMAS rule:
1. Division: $14÷2=7$

$$16\times 17-7\times 3=251$$

2. Multiplication:
* $16\times 17=272$
* $7\times 3=21$

$$272-21=251$$

3. Subtraction: $272-21=251\to 251=251$ $

Since LHS matches RHS, Option A is the correct combination.