5c3= Invalid circle
220-10=210
but only one circle out of 10 is valid , 211 answer
I think you mean the right things here; complete sentences would help us understand you. You are saying that there are 12C3 = 220 sets of 3 points; but 5C3 = 10 of them all lie on the same circle, so we subtract 10 and add 1 back in order to count the circle only once. Good.
I did not understood that i have to count circles exactly only with 3 points .
I thought atleast means they are telling minimum 3 maximum can be any no less than 12.
This makes little grammatical sense.
I think you are referring to the phrase in the problem, "circles that can be drawn through
at least 3 of these points". Since any 3 points determine a circle, we can draw a circle through
any three points, but such a circle might also pass through others. They are saying that they are
not excluding circles that pass through
more than 3 points. But the only circle that does that is that one 5-point circle.
Weak English translation costs me lot of time
I'm not sure whether you (or pka) are referring to your having to
read problems in English (which I presume were written in English originally, but not always well), or your having to
write to us in English (making it often quite hard both for you to express yourself clearly, and for us to understand your thinking). But both of those, and more, do indeed cost all of us time.
As for your writing, I find that if you (any non-native speaker) say more than you think you need to say, expressing the same ideas in more words and in multiple ways, it is commonly easier to be understood. (Too many try to use fewer words than they need, because even a few words requires effort, and perhaps they think that fewer words mean fewer embarrassing mistakes.) That's what I would try to do if I had to write in an unfamiliar language! It does slow down the initial writing, but it may reduce the need for back-and-forth communication.
