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JEE Main 20244 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
4 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2024 · 4 April · Morning Shift · Mathematics · Permutation and Combination

There are 5 points P_1, P_2, P_3, P_4, P_5 on the side A B ,...

There are 5 points P1,P2,P3,P4,P5P_1, P_2, P_3, P_4, P_5 on the side ABA B, excluding AA and BB, of a triangle ABCA B C. Similarly there are 6 points P6,P7,…,P11\mathrm{P}_6, \mathrm{P}_7, \ldots, \mathrm{P}_{11} on the side BC\mathrm{BC} and 7 points P12,P13,…,P18\mathrm{P}_{12}, \mathrm{P}_{13}, \ldots, \mathrm{P}_{18} on the side CAC A of the triangle. The number of triangles, that can be formed using the points P1,P2,…,P18\mathrm{P}_1, \mathrm{P}_2, \ldots, \mathrm{P}_{18} as vertices, is :

Options

  1. A776
  2. B796
  3. C751
  4. D771

Correct answer

C. 751

Step-by-step solution

18C3−5C3−6C3−7C3=751\begin{aligned} & { }^{18} \mathrm{C}_3-{ }^5 \mathrm{C}_3-{ }^6 \mathrm{C}_3-{ }^7 \mathrm{C}_3 \\ & =751\end{aligned}
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