<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 determined by pairs of these 6 points?</p>
<p>A)15
B)18
C)20
D)30
E)36</p>
<p>For problems such as these, I usually resort to drawing and connecting the dots, counting each as I go along (hoping that I don't miss a number). This method can get confusing if there is a lot of dots/material.</p>
<p>So, how do you solve this kind of problem without drawing an image?</p>
<p>is this from bb?</p>
<p>its A right?
I just quickly drew it but I think its combination? so 6C2</p>
<p>Is the answer A? The first point can connect to each of the other 5 points and form 5 lines. The second point can now only connect with 4 other points and form 4 more, unique lines. etc…</p>
<p>5+4+3+2+1=15</p>
<p>Here’s my first approach. Find the pattern.
2 points on a plane. 1 line.
3 points on a plane. 3 lines.
You might have to do more, but from the 3 points, I already found the pattern.</p>
<p>Basically, 2 points make a line, so there’s two “slots” available.
For 2 points, 2 1 = 2 permutations. 2perm/2 = 1 line (combination).
For 3 points, 3 2 = 6 permutations. 6/2 = 3 lines.
For 4 points, 4 3 = 12 permutations. 12/2 = 6 lines.
6 points, 6 5 = 30 permutations. 30/2 = 15 combinations/lines.</p>
<p>Yes, the answer is A. No, it’s not from the BB, it’s QaS.</p>
<p>Does the clause “no 3 of which lie on the same line” mean that a line can’t go through three points? If so, when I draw it I only get 13. The two lines on the end go through 3 points.</p>
<p>Anyways, I guess the nCr function works. nCr(6,2)=15.</p>
<p>When you see a problem that might at first tempt you to draw it all out, check the answer choices. If the smallest amount is 15, you should probably find a different approach that would be faster.</p>
<p>You can solve this problem with a basic knowledge of combinations, which proves to be quite handy on standardized tests. </p>
<p>You have 6 points, and you need two points for a line. Thus, its basically like seeing how many ways you can get 2 things out of 6, where the order in which you pick the two points does not matter. </p>
<p>If you know the formula, or you use some probability reasoning, the answer will be (6 * 5)/(2) or 6C2 or 15.</p>
<p>How do you know when to use a combination or a permutation?</p>
<p>If the order of the sets doesn’t matter, use combinations. If it does matter i.e. specific arrangements with certain qualities attributed to each distinct formation, use permutations.</p>
<p>i just thought of a hexagon, and connected them mentally. hopefully thats allowed :)</p>
<p>Don’t you learn this type of thing in elementary school? 6 points each with lines to the other points. One point has five new lines the next has 4 new lines, the next 3 and so on.</p>
<p>You shouldn’t even have to think about permutations and combinations for this.</p>