How many words of $4$ distinct letters can be formed using the letters of the word $DHOLPUR$ if $L$ and $P$ are always excluded?

If all the seven letters of the word $LEADING$ are permuted in all possible ways and the words thus formed are arranged as in the dictionary order,then the word in $2017^{\text{th}}$ place is

$A$ coin is tossed $3$ times and the outcomes are recorded. How many possible outcomes are there?

How many numbers can be formed using the digits $0, 1, 2, 3, 4, 5$ that are greater than $3000$ (repetition is not allowed)?

$A$ dictionary is printed consisting of $7$-lettered words only that can be made using the letters of the word $CRICKET$. If the words are arranged in alphabetical order,as in an ordinary dictionary,then the number of words before the word $CRICKET$ is:

All the letters of the word $ABRACADABRA$ are arranged in different possible ways. The number of such arrangements in which the vowels are together is: