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

The number of ways in which $6$ distinct rings can be worn on the $4$ fingers of one hand is:

Out of $5$ apples,$10$ mangoes,and $15$ oranges,$15$ fruits are to be distributed between two persons. Find the total number of ways of distribution.

$\binom{n}{n-r} + \binom{n}{r+1}$,whenever $0 \le r \le n-1$,is equal to

The number of numbers between $2,000$ and $5,000$ that can be formed using the digits $0, 1, 2, 3, 4$ (repetition of digits is not allowed) which are multiples of $3$ is?

Out of $6$ boys and $4$ girls,a group of $7$ is to be formed. In how many ways can this be done if the group is to have a majority of boys?