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Combinations Question Moderate
Solution We know, a triangle will be formed by taking three points at a time..'.Required number of triangles =12C3−7C3 =12× 11×103×2×1−7×6×53×2=220−35=185
Get the answer to your homework problem. Try Numerade free for 7 days Maria G. Algebra 6 months, 1 week ago We don’t have your requested question, but here is a suggested video that might help. There are 15 points in a plane of which 8 of them are ot a straight line. Then how many (i) straight lines can be formed? (A) 105 (B) 21 (C) 78 (D) 288 (ii) triangles can be formed? (A) 399 (B) 400 (C) 234 (D) 72 Free 10 Qs. 10 Marks 10 Mins Concept: If n points are there in a plane and none of the 3 are collinear then, Number of triangles formed = nC3 Formulas used:
Number of triangles formed by 12 points = 12C3 But, 7 points are collinear, so triangles cannot be formed. And hence, the number of triangles which could not be formed by these 7 points mutually should be removed. ∴ Number of triangles formed will be = 12C3 – 7C3 = 220 – 35 = 185 India’s #1 Learning Platform Start Complete Exam Preparation Video Lessons & PDF Notes Get Started for Free Download App Trusted by 3,12,37,300+ Students Text Solution 185175115105 Answer : A Solution : To form a triangle, we need 3 points. 12 points are given. <br> So, `.^(12)C_(3)` triangle can be formed ltbr. But, givne that 7 points are on a straight line. Selecting 3 points from this set will not form a triangle <br> So, number of triangle formed `.^(12)C_(3) - .^(7)C_(3)` <br> `= (12!)/(3!9!) - (7!)/(3!4!)` <br> `= (12 xx 11 xx 10 )/(3 xx 2 xx 1) - (7 xx 6 xx 5)/(3 xx 2 xx 1) = 220 - 35 = 185` Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now Uh-Oh! That’s all you get for now. We would love to personalise your learning journey. Sign Up to explore more. Sign Up or Login Skip for now 185175115105 Answer : A Solution : To form a triangle, we need 3 points. 12 points are given. <br> So, `.^(12)C_(3)` triangle can be formed ltbr. But, givne that 7 points are on a straight line. Selecting 3 points from this set will not form a triangle <br> So, number of triangle formed `.^(12)C_(3) - .^(7)C_(3)` <br> `= (12!)/(3!9!) - (7!)/(3!4!)` <br> `= (12 xx 11 xx 10 )/(3 xx 2 xx 1) - (7 xx 6 xx 5)/(3 xx 2 xx 1) = 220 - 35 = 185` How many triangles can be formed by choosing the vertices from the set of 12 points seven of which lie on the same line?Solution. The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is 185. So, these seven points will form no triangle.
How many triangles can be made by joining 12 points in a plane given that 7 are in one line?How many triangles can be formed by joining 12 points, 7 of which are collinear? The number of triangles that can be formed from 12 points is = 10 as 7 points are collinear. E is the answer.
What is the number of triangles that can be formed by choosing the vertices from a set of 11 points in a plane seven of which lie on the same straight line?Therefore, required number of triangles =12C3−7C3=220−35=185.
What is the number of triangles that can be formed whose vertices are the vertices of an octagon?This way, we have 4 triangles for each side of the octagon. Thus, there are 8 x 4 = 32 such triangles. Was this answer helpful?
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