JEE PYQ: Permutation And Combination Question 3
Question 3 - 2021 (17 Mar Shift 2)
If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to:
(1) 364
(2) 240
(3) 333
(4) 360
Show Answer
Answer: (3)
Solution
Total triangles $= {}^{14}C_3 - {}^3C_3 - {}^5C_3 - {}^6C_3 = 364 - 1 - 10 - 20 = 333$.