In how many ways can the squares of a 4 2 grid (4 rows and 2 columns) be filled with the letters of the word 'SPHERE' such that each row contains at least one letter?

Step-by-step solution

The word 'SPHERE' consists of 6 letters, in which 'E' appears twice and the rest are distinct. The given grid has 4 rows and 2 columns, making a total of 8 squares. Since there are 6 letters to be placed in 8 squares, exactly 2 squares will remain empty. The condition states that each row must contain at least one letter. This implies that no row can be completely empty. A row is completely empty if and only if both of its squares are empty. The total number of ways to choose 2 empty squares out of the 8 squares is