For the equation in the grid pathing problem, which calculation accounts for duplicate moves?

In grid pathing problems, particularly those that involve counting unique paths while accounting for duplicate moves, it's essential to utilize combinatorial mathematics. The correct answer involves multiplying by the factorial of each type of move because this approach effectively removes the duplicity by acknowledging the number of ways to arrange the identical moves.

When you are calculating the total number of unique paths in a grid, particularly when you have multiple moves in the same direction (like moving right or down), each sequence of moves can be rearranged in various ways. For example, if your path consists of five moves to the right and three moves down, simply counting all possible sequences of eight moves would result in counting many identical paths multiple times.

By using the factorial of each type of move, you can determine how many unique arrangements of these moves are possible. This is mathematically represented as:

• Total number of moves factorial divided by the factorial of each type of move.

This method ensures all possible arrangements of the moves are counted, while duplicates arising from identical moves are effectively discounted, leading to the final count reflecting only unique paths from the start to the endpoint on the grid.

Using this combinatorial principle ensures the accurate counting of paths without overcounting due to duplicated movements, hence affirm