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

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

Let A be a set containing n elements. A subset P of A is chosen, and the set A is reconstructed by replacing the elements of P. A subset Q of A is chosen again. The number of ways of choosing P and Q such that Q contains just one element more than P is