Doubt from permutation and combination

[Azimuddin_2019]

There are arbitrary 7 points in the plane. Circles are drawn through every 4 possible concyclic points. Find the maximum number of circles that can be drawn ? Anyone confirm what they got as answer , integer type question 0 to 9

[Azimuddin_2019]

Anyone try ??

[arush_2019]

Why isn't it 7C4

[Azimuddin_2019]

If u r thinking that way , just make a figure utilize it and try to get 7c4 circles @arush_kumar_singh bro

[arush_2019]

Is it 3
@Azimuddin_Sheikh

[Siddhant_2019]

I am getting 5 by drawing

[Azimuddin_2019]

Answer is 6 or 7 just wanna know which is correct @Siddhant_Mudholkar @arush_kumar_singh

[Lavesh_2020]

Since we want to have max. no of circles, we assume that no three points are co-linear. Having that said, Circles can be formed from any four points in 7C4 ways and now we have to subtract those circles which are made from 5 points & 6 points & all 7 points. (There will be over lapping cases in these too.)

We have not been taught sets, venn diagram. If someone has been taught that, give this method a try.

[arush_2019]

Getting 7
4+3
Is it correct approach????

[Lavesh_2020]

What about circles formed from one of the first considered point and three of the newly considered points. That isn't counted right?

[arush_2019]

@Lavesh_Gupta
But for every 3 pts circle is fixed

[Mayank_2019_1]

But shouldn't there be 4 points on every circle ?

Circles are drawn through every 4 possible concyclic points.

[Azimuddin_2019]

Total number of ordered pairs (m,n) where m and n are positive integers such that \frac {n^3 + 1}{mn - 1} is an integer. I am getting 9 , can anyone confirm ??

[Azimuddin_2019]

Also this question : A triangle is cut randomly from a piece of paper. What is the probability that it is an right triangle?
Answer given is zero , can anyone show how its correct ??

[Lavesh_2020]

Isn't the probability zero for unequal events. For eg: the probability of a fan hanging from the ceiling is zero or else half of the fans should fall from ceiling.

This is just a tukka as we haven't been taught probability yet.

P.S. How do I change Class 11 Student to Class 12 student @Bansal Classroom??

[Azimuddin_2019]

@Lavesh_Gupta Bro , then what is the probability that triangle is acute ?? Can u tell

[Lavesh_2020]

1/2?

[Azimuddin_2019]

Nope @Lavesh_Gupta bro I have proved it to be 1/4 ,and answer is correct , one of the parts from the comprehension .( bro isnt there any option for class change , check settings )

[Lavesh_2020]

How? A triangle can either be acute or obtuse? (Or right) Bhaiya can you explain?

[Azimuddin_2019]

Its not the case u r thinking off @Lavesh_Gupta , it different we have to form a triangle from a paper and it can be acute or obtuse or right angle .I thought of graphically. Got 3/4 for obtuse ( wait I will share my approach in one hour )