How many words can be made from the letters of the word $DELHI$,if $L$ comes in the middle in every word?

$X, Y, Z$ are sets of all positive divisors of $10^{60}, 20^{50}$ and $30^{40}$ respectively. Find $n(X \cup Y \cup Z)$.

In how many ways can $10$ balls be divided between two boys,if one receives two balls and the other receives eight balls?

The total number of selections of the letters in the phrase "ned needs nineteen nets" is:

If $33!$ is divisible by $2^n$,where $n \in N$,then the sum of all possible values of $n$ is:

In an examination,there are three multiple-choice questions,and each question has $4$ choices. The number of ways in which a student can fail to get all answers correct is: