All the letters of the word MOTHER are arranged in all possible ways and the resulting words (may or may not have meaning) are arranged as in the dictionary. The number of words that appear after the word MOTHER is

The number of positive integral solution of $\frac{1}{x}+\frac{1}{y}=\frac{1}{2025}$ is

The number of positive integral solutions of $x y z=60$ is

5 boys and 5 girls have to sit around a table. The number of ways in which all of them can sit so that no two boys and no two girls are together is