How many words can be formed by using all the letters of the word '$TRIVANDRUM$' using each letter exactly once (in $!$)?

The number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets among themselves such that they get consecutive blocks of $5, 3$ and $2$ tickets is:

There are two urns. Urn $A$ has $3$ distinct red balls and urn $B$ has $9$ distinct blue balls. From each urn,two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

In how many different ways can the letters of the word $TABLE$ be arranged?

In a certain test,there are $n$ questions. In the test,$2^{n-i}$ students gave wrong answers to at least $i$ questions,where $i = 1, 2, \dots, n$. If the total number of wrong answers given is $2047$,then $n$ is equal to

How many $5$-digit even numbers can be formed using the digits $1, 2, 5, 5, 4$?