$n$ 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

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 total number of seven-digit numbers whose sum of digits is even is

The number of all five-letter words (with or without meaning) having at least one repeated letter that can be formed by using the letters of the word $INCONVENIENCE$ is:

From $6$ different novels and $3$ different dictionaries,$4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

Statement-$1$: The number of $4$-digit numbers that can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ which are divisible by $4$ is $200$.
Statement-$2$: $A$ number is divisible by $4$ if its unit digit is divisible by $4$.