The number of straight lines that can be formed by joining $20$ points,no three of which are in the same straight line,except $4$ of them which are in the same line.

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

There are $4$ notes of Rs. $100$ and $5$ other notes of denominations Rs. $1$,Rs. $2$,Rs. $5$,Rs. $20$,and Rs. $50$. These notes are to be distributed among $3$ children such that each child receives at least one note of Rs. $100$. Find the total number of ways of distribution.

The number of $6$-digit numbers that can be formed using the digits $0, 1, 2, 5, 7,$ and $9$ which are divisible by $11$ and no digit is repeated,is

The total number of possible ways in which a person can go from point $A(0,0)$ to point $B(3,3)$ if they can travel only to the right or upward along the grid lines is equal to:

In how many ways can $5$ boys and $5$ girls sit in a circle so that no two boys sit together?