There are $n$ points in a plane of which $p$ points are collinear. How many lines can be formed from these points?

$P_1$ and $P_2$ are two distinct and intersecting planes. Three non-collinear points lie on $P_1$ and another three non-collinear points lie on $P_2$ (none being on the line of intersection of the planes). Then,the maximum number of tetrahedrons formed using these six points is:

In how many ways is it possible to choose a white square and a black square on a chess board so that the squares do not lie in the same row or column?

$n$ balls each of weight $w$ are weighed in pairs. The sum of the weights of all possible pairs is $120$. When they are weighed in triplets,the sum of the weights of all possible triplets is $480$. Then $n$ is:

$A$ candidate is required to answer $6$ out of $10$ questions,which are divided into two groups each containing $5$ questions. The candidate is not permitted to attempt more than $4$ questions from each group. In how many ways can the candidate make their choice?

The number of different words that can be formed out of the letters of the word $MORADABAD$ taken four at a time is