$10$ different letters of the English alphabet are given. Out of these letters,words of $5$ letters are formed. How many words can be formed if at least one letter is repeated?

How many numbers between $999$ and $10,000$ can be formed using the digits $0, 2, 3, 6, 7, 8$ without repetition?

Find the number of permutations of the letters of the word $ALLAHABAD$.

The total number of permutations of the letters of the word "$BANANA$" is

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

How many $3$-digit numbers can be formed from the digits $1, 2, 3, 4,$ and $5$ assuming that repetition of the digits is not allowed?