There is a 5 × 5 square grid, with each of its cells having a distinct identity. In how many ways can three identical coins be placed in the grid (with at most one coin in each cell) such that no two coins are placed either in the same row or in the same column?

This problem can be solved using the principle of permutations and combinations. Here are the steps:

1. Choose 3 distinct rows for the coins from the 5 available. This can be done in 5C3 ways. The notation "nCr" represents the number of combinations of n items taken r at a time. So, 5C3 = 10.

2. Having chosen the rows, we now choose 3 distinct columns for the coins from the 5 available. This can also be done in 5C3 ways. So, 5C3 = 10.

3. Now, we have 3 coins and 3 cells (one in each chosen row and column). The number of ways to arrange these 3 coins in 3 cells is 3! (3 factorial), which equals 6.

4. Therefore, the total number of ways to place the coins is the product of the above three quantities, which is 10 * 10 * 6 = 600.

So, there are 600 ways to place three identical coins in the grid such that no two coins are placed either in the same row or in the same column.