## virtus 3 years ago 9 dots are drawn as below. How many triangles can be formed by joining three dots?

1. virtus

|dw:1342275033333:dw|

2. virtus

@UnkleRhaukus hope your not here to troll me again

3. UnkleRhaukus

thats not my style @virtus

4. UnkleRhaukus

i can see four 2x2 triangles

5. UnkleRhaukus

16, 1x1 triangles

6. UnkleRhaukus

i suppose the dont have to be right angles

7. ash2326

@virtus do you have options?

8. virtus

not sure what you mean by options @ash2326 but incase you were wondering, my solution book says 9C3 -8

9. virtus

@UnkleRhaukus you have PARTIALLY redeemed yourself

10. UnkleRhaukus

11. virtus

good to know, why don't you change feeling "good" to "euphoric" by suggesting why the answer is 9C3 -8

12. UnkleRhaukus

say you want to find all the triangle that have the top left as a vertex, how many can you make

13. mukushla

9C3 -triples which are in the same line=9C3-8 |dw:1342275604359:dw|

14. UnkleRhaukus

i count eighteen |dw:1342275638118:dw|

15. UnkleRhaukus

19,20|dw:1342275746454:dw|

16. UnkleRhaukus

there are so many

17. virtus

but hows that joining three dots?

18. UnkleRhaukus

mukushla is right , we are misusing the straight lines because they are not triangles

19. mukushla

different triangles can be formed by joining 3 of the dotes unless 3 dots are in the same line, so C(3,9)-8

20. virtus

but why is do we minus 8

21. virtus

*why do we

22. mukushla

u can count triples of dots that are in the same line just like what i did up there

23. UnkleRhaukus

this is not a triangle |dw:1342276198984:dw|

24. virtus

oh ok

25. sarthak810

6

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