How many words can be formed using the letters of the word $INDEPENDENCE$,such that all vowels always come together?

The number of five-digit numbers greater than $50000$ that can be formed by using all the digits $0, 1, 3, 5, 9$ only once is

If $a$ denotes the number of permutations of $(x + 2)$ items taken all at a time,$b$ denotes the number of permutations of $x$ items taken $11$ at a time,and $c$ denotes the number of permutations of $(x - 11)$ items taken all at a time. If $a = 182bc$,find the value of $x$.

$8$-digit numbers are formed using the digits $1, 1, 2, 2, 2, 3, 4, 4$. The number of such numbers in which the odd digits do not occupy odd places is:

Let $P$ be the set of seven-digit numbers with the sum of their digits equal to $11$. If the numbers in $P$ are formed by using the digits $1, 2,$ and $3$ only,then the number of elements in the set $P$ is:

The number of ways of forming a queue of $4$ boys and $3$ girls such that all the girls are not together, is: