Eight different letters of an alphabet are given. Words of four letters from these are formed. The number of such words with at least one letter repeated is:

How many numbers greater than $1000000$ can be formed by using the digits $1, 2, 0, 2, 4, 2, 4$?

How many numbers less than $1000$ can be formed using the digits $0, 1, 2, 4,$ and $5$ if repetition of digits is not allowed?

Given $5$ flags of different colours,how many different signals can be generated if each signal requires the use of $2$ flags,one below the other?

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 $x$.

If the best and the worst paper never appear together,then in how many ways can $6$ examination papers be arranged?