<p>Any 2 points determine a line. If there are 6 points in a plane, no 3 of which lie on the same line, how many lines are determine by pairs of these 6 points?</p>
<p>So I pout 30 ( I know it's 15 stupid mistake). I am wondering though the way too get 15 (I counted after). I know its a permutation so 6x5, but then why would you divide by two? Could someone explain why it is needed to do this?</p>
<p>You should devide by two because 6x5 all the possible lines that are determined by these 6 points.But you know that lines AB and BA ,as well as BC and CB ,and RT - TR are the same.Thats why you should devide :)</p>
<p>Right. In other words, it's a combination, not a permutation. Combinations are like permutations except order doesn't matter. AB and BA are the same line, thus, you divide by two to account for your double counting of AB and BA as two different lines.</p>
<p>Keep in mind,that if you are asked to find the number of VECTORS determined ,you WILL NOT devide by two,because AB and BA are DIFFERENT vectors :)</p>