What is the number of triangles formed by joining 12 points 7 of which are in the same straight line?
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. Show
Explanation: Total number of triangles formed from 12 points taking 3 at a time = 12C3 But given that out of 12 points, 7 are collinear So, these seven points will form no triangle. ∴ The required number of triangles = 12C3 – 7C3 = `(12!)/(3! 9!) - (7!)/(3!4!)` = `(12 xx 11 xx 10 xx 9!)/(3 xx 2 xx 1 xx 9!) - (7 xx 6 xx 5 xx 4!)/(3 xx 2 xx 1 xx 4!)` = `(12 xx 11 xx 10)/(3 xx 2) - (7 xx 6 xx 5)/(3 xx 2)` = 220 – 35 = 185 If 7 points out of 12 are in the same straight line, then the number of triangles formed is(A) 19(B) 158(C) 185(D) 201Answer Verified
Hint: First of all, find the ways formed triangles by 12 points that is \[{}^{12}{C_3}\] then after 7 points are in a straight line so find the ways formed triangles by 7 points that is \[{}^7{C_3}\]then subtract this from \[{}^{12}{C_3}\] so, we get the answer. Complete step by step solution: $\therefore$ The number of triangles formed is 185. Note: Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Solution The correct option is A185Explanation for the correct option:Calculate the number of triangles that can be formed.We are given, 12 set of points.Number of triangles formed with 12 points = C312But, according to the given condition, 7 points lie on the same straight lineThus, the selection of 3 points out of 7 collinear points =C37, which we need to deduct from the non-collinear points.Thus, the required number of triangles =C312–C3 7=220-35=185Hence, Option (A) is the correct answer. (adsbygoogle = window.adsbygoogle || []).push({});Textbooks Question Papers Home How many triangles can be formed by joining 12 points 7 of which are collinear?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.
How many triangles can be formed by joining 16 points out of which 7 are collinear?And hence, the number of triangles which could not be formed by these 7 points mutually should be removed. = 12 !
How many triangles can be formed by joining 12 points 4 of which are collinear?Solution : Number of triangles `=(. ^(12)C_(3)-. ^(4)C_(3))=(220-4)=216`. Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
How many triangles can be formed using a 12 non collinear points in a plane?1 Answer. Show activity on this post. If no three points in the set are collinear, then similarly we can choose any two points other than A to be other two vertices of a triangle. Hence the answer is C(11,2).
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