Discussion

Explanation:

Consider the solution to the previous question.

A → B: To go from A to B, we need to take 4 steps towards right and 4 steps upwards i.e., total number of ways = $\frac{8!}{4!\times 4!}$

B → C: To go from B to C, we need to take 4 steps towards right and 4 steps upwards i.e., total number of ways = $\frac{8!}{4!\times 4!}$

A → B → C: To go from A to C via B, total number of ways = $\frac{8!}{4!\times 4!}\times \frac{8!}{4!\times 4!}$ =  $\frac{{\left(8!\right)}^2}{{\left(4!\right)}^4}$.

Hence, option (a).

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