permuatation ques

[sspms2002]

How many Triangles can be formed from 8 points out of which 3 are collinear??

i only have ans..no explaination...so please explain ur ans too..

[newton9]

8C3 - 3C3

I guess 55 is the answer.

[neoreaves]

IMO 15


3 are linear points lets say a,b ,c



a ----b ----c


so there are 5 non linear points thus if we use side a-b then we can form 5 triangles.

with b-c similarly we can form 5 triangles

a-c = 5

so total = 15

[sspms2002]

The answer given is 5C3 + 8 *3C2 + 3C1 * 5C2

But iam unable to comprehend it...Pls help

[eaakbari]

We have 8 points 3 collinear and 5 not collinear.
There are 3 possibilities.

Triangle is made from 5 non collinear points - 5C3
Triangle is made using one collinear point and 2 non collinear - 3C1 * 5C2
Triangle is made using two collinear points and 1 non collinear - 3C2 * 5C1

So answer is 5C3 + 3C1*5C2 + 3C2*5C1

I think you might have made a typo and written 8 instead of 5. Please clarify and give source of question

E

[pops]

what is incorrect with 8C3 - 1 ?
triangle is formed by any 3 points, so we select any 3 points by 8C3. Then we remove 1 case where 3 collinear points were selected. Hence 8C3-1=55

[eaakbari]

According to me that too is correct it does match with my answer. But do want to wait for sspms2002's reply as his answer seems wrong.