Five balls of different colours are to be placed in three boxes of different sizes. The number of ways in which we can place the balls in the boxes so that no box remains empty is

$$ \text { If } 1000!=3^n \times m \text { where } m \text { is an integer not divisible by } 3 \text {, then } n= $$

The number of ways in which the letters of the word 'VERTICAL' can be arranged without changing the order of the vowels is

n objects are distributed at random among n persons. The number of ways in which this can be done so that at least one of them will not get any object is