In how many ways the letters of the word DIPESH can be placed in the squares of the adjoining figure so that no row remains empty?

Explanation

If all letters are same, then number of ways
=Coefficient of `x^(6)` in `(.^(3)C_(1)x+.^(3)C_(2)x^(2)+.^(3)C_(3)x^(3))^(3)(.^(1)C_(1)x)^(2)`
=Coeficient of x in `(3+3x+x^(2))^(3)`
=Coefficient of x in `(3+3x)^(3)` [neglecting higher degree term]
`=27xx.^(3)C_1=81`
But inn DIPESH all letters are different.
`therefore`Required number of ways`=81xx6!`