Problem Solving

How many triangles can be drawn with 17 points, if 5, 7 and 8 of them are in three different lines? The three lines intersect each other in pairs.
1. 680
2. 136
3. 569
4. 171

Where did you find that problem?

srcc25anu wrote:How many triangles can be drawn with 17 points, if 5, 7 and 8 of them are in three different lines? The three lines intersect each other in pairs.
1. 680
2. 136
3. 569
4. 171

srcc25anu wrote:How many triangles can be drawn with 17 points, if 5, 7 and 8 of them are in three different lines? The three lines intersect each other in pairs.
1. 680
2. 136
3. 569
4. 171

Number of 3 point combinations = 17C3 = 680

Of these there are several 3-point combinations that lie on a straight line and do not form a triangle, so we need to discount them.

Number of 3 point combinations that lie on a straight line = 8C3 + 5C3 + 7C3 = 101

Thus number of unique triangles = 680 - 101 = 579

This is a really tough problem. What's the OA ?

Stormier - I too got the same answer 579 using the same methodology that u have applied. the OA is 569 though.
Tomada - And i dont exactly recall the source of this problem .... just happened to come across it on some forum.

stormier wrote:

srcc25anu wrote:How many triangles can be drawn with 17 points, if 5, 7 and 8 of them are in three different lines? The three lines intersect each other in pairs.
1. 680
2. 136
3. 569
4. 171

Number of 3 point combinations = 17C3 = 680

Of these there are several 3-point combinations that lie on a straight line and do not form a triangle, so we need to discount them.

Number of 3 point combinations that lie on a straight line = 8C3 + 5C3 + 7C3 = 101

Thus number of unique triangles = 680 - 101 = 579

This is a really tough problem. What's the OA ?