Question:

ABCD is a convex quadrilateral. 3, 4, 5 and 6 points are marked on the sides AB, BC, CD and DA respectively . The number of triangles with vertices on different sides is

Updated On: Jul 6, 2022
  • 270
  • 320
  • 282
  • 342
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The Correct Option is D

Solution and Explanation

Triangles with vertices on AB, BC and CD are $3?4?5 = 60$ Triangles with vertices on AB, BC and DA are $3?4?6 = 72$ Triangles with vertices on AB, CD and DA are $3?5?6 = 90$ Triangles with vertices on BC, CDand DA are $4?5?6 = 120$ $\therefore$ Total no. of triangles $= 60 + 72 + 90 + 120 = 342$
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Notes on permutations and combinations

Concepts Used:

Permutations and Combinations

Permutation:

Permutation is the method or the act of arranging members of a set into an order or a sequence. 

  • In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point. 
  • A permutation is used in many events of daily life. It is used for a list of data where the data order matters.

Combination:

Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.

  • Combination refers to the combination of about n things taken k at a time without any repetition.
  • The combination is used for a group of data where the order of data does not matter.