How many triangles can be formed by joining 12 points, 7 of which are

Question

How many triangles can be formed by joining 12 points, 7 of which are collinear?

A. 255
B. 220 
C. 185
D. 35 
E. 10

Chethan92 · Answer

The number of triangles that can be formed from 12 points is  5C_3  = 10 as 7 points are collinear.

E is the answer.

Archit3110 · Answer

given 7 points are collinear ,which means 7 out of 12 points are on same line and 5 are random points

so total triangles which can be formed ; 7c2*5c1+7c1*5c2+5c3 = 21*5+7*10+10 = 185
IMO C

EgmatQuantExpert · Answer

Solution 
  Given:  
 • Total number of points = 12
 o Number of collinear points = 7

To find:  
 • The number of triangles that can be formed

Approach and Working:   
 • The number of triangles that can be formed, N = number of ways of selecting 2 points from 7 and the other from the remaining 5 + the number of ways of selecting 1 from 7 and 2 from the remaining 5 + the number of ways of selecting 3 points from the remaining 5
• Therefore,  N = ^7C_2 * ^5C_1 + ^7C_1 * ^5C_2 + ^5C_3 = 21 * 5 + 7 * 10 + 10 = 185

Hence, the correct answer is Option C

Answer: C

https://e-gmat.com/blogs/wp-content/uploads/2016/12/Geometry-Ability-Quiz-4-e1480581478957.png

TestPrepUnlimited · Answer

We can start with 12C3 to get  \frac{12*11*10}{3!} = 2*11*10  random selections.

The problem with that random selection is the 7 collinear points, if we pick 3 points on the same line it will not form a triangle so we need to eliminate 7C3 =  \frac{7*6*5}{3!} = 7*5  selections.

2*11*10 - 7*5 = 220 - 35 = 185.

Ans: C

shanky315 · Answer

We can solve by finding total triangles formed by 12 points and then subtract those by the total triangles formed by 7 points ( as they are collinear ).

12C3-7C3= 185. Hence,C

Posted from my mobile device

satish_sahoo · Answer

Total triangles that can be formed using the  12  points are  12C3 = 220 
But,  7  of these points are collinear, and hence can't be used to form triangles among themselves.

So, number of triangles that can't be formed are  7C3 = 35

220-35 = 185

Answer C.

m7runner · Answer

We can draw a line through the 7 points since they are collinear. Using this information, there are three cases:

→ Case 1: Choose two collinear points and another which isn't collinear =  7C_2 * 5C_1  = 105
→ Case 2: Choose one collinear point and two points which aren't collinear =  7C_1 * 5C_2  = 80
→ Case 3: Combine three points which aren't collinear =  5C_3  = 10
→ Total cases = 105+80+10 = 185.
→ Option C is the correct answer choice.

How many triangles can be formed by joining 12 points, 7 of which are

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

How many triangles can be formed by joining 12 points, 7 of which are

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards