Permutations an...

What is the number of diagonals of a heptagon?

12 points are marked on a circle. How many octagon can be formed joining these points.

There are 13 points in a plane of which 5 are collinear. Find the number of straight lines obtained by joining these points in pairs.

There are 4 flags of different colours and each can be used for signals. Determine how many signals can be sent using one or more flags at a time.

What is \(C(n, r)+2 C(n, r+1)+C(n, r+2)\) equal to?

If \({ }^{2 {n}} {C}_{3}:^{{n}} {C}_{3}=17: 2\), find \({n}\).

The number of ways in which 4 boys and 4 girls can be arranged in a row so, that no two girls and no two boys are together is:

If \(C(30, n-3)=C(30, n+3)\), then what is n equal to?

If \({ }^{2 n} P_{3}=100^{n} P_{2}\), then the value of \(n\) is:

In how many ways can a team of 5 players be selected from 8 players so as not to include a particular player?