In how many ways can $3$ letters be posted in $4$ letter boxes,if all the letters are not posted in the same letter box?

All the letters of the word $ANIMAL$ are permuted in all possible ways and the permutations thus formed are arranged in dictionary order. If the rank of the word $ANIMAL$ is $x$,then the permutation with rank $x$,among the permutations obtained by permuting the letters of the word $PERSON$ and arranging the permutations thus formed in dictionary order is

The number of ways of selecting $15$ teams from $15$ men and $15$ women,such that each team consists of one man and one woman,is

The number of $3$-digit odd numbers divisible by $3$ that can be formed using the digits $1, 2, 3, 4, 5, 6$ when repetition is not allowed is:

The difference between an integer $n$ and its cube $n^3$ is always divisible by which of the following?

The number of natural numbers,between $212$ and $999$,such that the sum of their digits is $15$,is . . . . . .