$A$ code word is to consist of $2$ English alphabets followed by $2$ distinct numbers between $1$ and $9$. For example,$CA23$ is a code word. How many such code words are there?

Let $S$ be the set of all triangles in the $xy$-plane,each having one vertex at the origin and the other two vertices lying on the coordinate axes with integral coordinates. If each triangle in $S$ has an area of $50$ sq. units,then the number of elements in the set $S$ is:

$6$ points in a plane are joined in all possible ways by indefinite straight lines. If no two lines are coincident or parallel,and no three lines pass through the same point (with the exception of the original $6$ points),the number of distinct points of intersection is equal to

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

Number of shortest paths from $HOSTEL$ to $ALLEN$ is equal to (as shown in the given figure):

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: