The number of ways in which a committee of $6$ members can be formed from $8$ gentlemen and $4$ ladies so that the committee contains at least $3$ ladies is:

We are to form different words with the letters of the word $INTEGER$. Let $m_1$ be the number of words in which $I$ and $N$ are never together and $m_2$ be the number of words which begin with $I$ and end with $R$,then $m_1/m_2$ is equal to

The total number of natural numbers of six digits that can be made with digits $1, 2, 3, 4$,if all digits are to appear in the same number at least once,is

There are $16$ points in a plane, out of which $6$ are collinear. How many lines can be drawn by joining these points?

If there are $6$ periods in each working day of a school,in how many ways can one arrange $5$ subjects such that each subject is allowed at least $1$ period?

If $(n+2)! = 2550(n!)$,find $n$.