In a circus,there are $10$ cages for $10$ animals. $4$ cages are so small that $5$ out of the $10$ animals cannot enter them. In how many ways can the $10$ animals be placed in the $10$ cages?

How many $4$-digit numbers are there with no digit repeated?

If $a$ denotes the number of permutations of $x + 2$ things taken all at a time,$b$ the number of permutations of $x$ things taken $11$ at a time,and $c$ the number of permutations of $x - 11$ things taken all at a time such that $a = 182bc$,then the value of $x$ is

All possible four-digit numbers are formed using the digits $0, 1, 2, 3$ such that no digit is repeated. The number of even numbers among them is

If all the possible $3$-digit numbers are formed using the digits $1, 3, 5, 7, 9$ without repeating any digit,then the number of such $3$-digit numbers which are divisible by $3$ is

The number of arrangements of the letters of the word $INDEPENDENCE$ in which all the vowels always occur together is