What's wrong with my reasoning ?
I am unable to understand the logic behind the following:-
The maximum number of points of intersection of 6 circles is ^{6}P_{2} = 30. I am unable to understand why are we using permutations. Maximum points of intersection of 2 circles is 2. So isn't the question about selecting 2 circles from 6 circles and the solution be ^{6}C_{2} = 15. Isn't this a question of combinations ? Where am I making an error ? What is the logic behind the rule ? Request advice on the above.
Thanks in advance !
Hello SheekhKebab,
There are 2 possibilities:
1) The circles overlap each other:- In this case there will be infinite points of intersection and the answer will be infinity.
2) None of the circles overlap each other:- In this case we select 2 circles in ^{6}C_{2} ways , but each pair of such circles selected intersect at 2 points. So we multiply the circles selected by 2:-^{6}C_{2} X 2 which is equivalent to ^{6}P_{2} to get the number of points of intersection.
But, you never mentioned which one is the case. You never mentioned whether the circles overlap or not. First, make sure you have got it right. Check your source.