Solved Examples

Displaying 1 - 5 of 8
  • Shortest Grid Path - Solving Permutation and Combination Questions

    Q: In the given figure, the lines represent one way roads allowing travel from any point, only to the up or to the left. Along how many distinct routes can a vehicle reach point B from Point A? (CAT 2004)(Possible answer choices provided - 15, 56, 120, 336)

     shortest path 3 by 5 grid


    Any explanation answer would tell you that this is a permutation with...

  • Team Selection - Solving Permutation and Combination Questions

    Q. A man has nine friends - four boys and five girls. In how many ways can he invite them, if there have to be exactly three girls in the invitees? (CAT 1996)(Given possible answer choices - 320, 160, 80, 200)


    This is a pure selection problem, the arrangement is inconsequential. If 3 girls are selected from 5 girls, then the arrangement of the three girls is insignificant and only the selection is important. Thus Combination is involved. Three girls always have to be...

  • Forming Triangles - Solving Permutation and Combination Questions

    Q. How many triangles can be formed by joining 12 points, 7 of which are collinear? (Answer choices provided - 220, 35, 10, 185)

    Ans. In this situation, if three points are selected to form a triangle, then these three form the same set of points even if they are arranged differently. Thus arrangement does not matter and so we use Combination here.

    Given data: total 12 points, 7 are collinear, 5 are non collinear.

    To solve this, find out all the ways three points can be joined to form a...

  • Circular Arrangement - Solving Permutation and Combination Questions

    Q. In how many ways can eight directors, the vice-chairman and chairman of a firm be seated at a round table, if the chairman has to sit between the vice-chairman and the director? (CAT 1997)(Possible answer choices provided - 9! * 2, 2 * 8!, 2 * 7!, none of these)


    In a circular arrangement problem, we always fix one position and the look at ways of arranging the rest with respect to the fixed position.

    Case 1 - seating of chairman - In this...

  • Balls and Boxes - Solving Permutation and Combination Questions

    How to solve Permutation and Combination questions involving balls and boxes? 

    The approach towards solving Permutation and Combination problems will be depicted through the solved examples below.

    Q: Boxes numbered 1, 2, 3, 4 and 5 are kept in a row and they are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. The how many different arrangements are possible, given that all balls of a given color are exactly identical in all respects?...