Permutations and Combinations
1 Board Maths previous year questions on Permutations and Combinations — options free on every question; 1 include the answer & explanation free, the rest unlock with PYQ Pass.
Q1 FREE PREVIEW
PYQA triangle PQR is such that 3 points lie on the side PQ,4 points on QR and 5 points on RP respectively. Triangles are constructed using these points as vertices. What is the number of triangles so formed?
✓ Correct answer: a)
205
Explanation
Total points are 12 on the three sides of triangle of which 3 points are collinear on side PQ,
4 points are collinear on side QR, 5 points are collinear on side PR,
Hence total number of triangles formed
\(={}^{12}C_{3}-{}^{3}C_{3}-{}^{4}C_{3}-{}^{5}C_{3}\\ =220-1-4-10\\ =205\)
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