How many words can be formed using the letters of the word $COMMITTEE$?

To fill $12$ vacancies,there are $25$ candidates,of which $5$ are from the scheduled caste. If $3$ of the vacancies are reserved for scheduled caste candidates while the rest are open to all,then the number of ways in which the selection can be made is:

The number of integers between $1$ and $10^{10}$ (inclusive) that contain the digit $1$ is:

The number of ways in which the letters of the word $TRIANGLE$ can be arranged such that no two vowels occur together is

In a certain test,${a_i}$ students gave wrong answers to at least $i$ questions,where $i = 1, 2, 3, ..., k$. No student gave more than $k$ wrong answers. The total number of wrong answers given is:

The number of ways in which $10$ persons can go in two boats so that there may be $5$ on each boat,supposing that two particular persons will not go in the same boat is: