The digits $4, 5, 6, 7, 8$ are written in every possible order. The number of numbers greater than $56000$ 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 $x$.

$_{n-1}P_r + r \cdot (_{n-1}P_{r-1}) = \dots$

The letters of the word $ARRANGE$ are used to form different words. All these words are arranged in dictionary order. What is the rank of the word $ARRANGE$ in the dictionary?

How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if each digit appears not more than once in each number?

The sum of all $4$-digit numbers that can be formed by using the digits $2, 4, 6, 8$ (repetition of digits not allowed) is