The number of diagonals of a polygon is 20. Find the number of its sides

  How many diagonals does a ten sided polygon have? How many triangles can be got by joining its vertices?

  Ram has 5 friends. In how many ways can be invite one or more of them to a party?

  A man has 6 friends. In how many ways can be invite one or more of them to a party?

  A committee of 5 is to be selected from among 6 boys and 5 girls. Determine the number of ways of selecting the committee if it is to consist of at least 1 boy and 1 girl?

  in an examination, a question paper consists of 12 questions divided into two parts I and II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the question?

  In how many ways can 6 beads of different colours form a necklace?

  In how may ways can 5 persons A, B, C, D and E sit around a circular table if a) B and D sit next to each other? b) A and D do not sit next to each other?

  Five girls and five boys are to be seated on a bench with the boys and girls alternating. Find the number of ways of their seating. In how many different ways could they sit around a circular table so that the boys and girls alternate?

  In an examination, a candidate has to pass in each of four subjects taken by him. In how many ways can he fail?