SOLUTION: 1. If there are 7 points in a plane, no three of which are collinear, how many distinct lines can be formed by connecting two of those points> a. 18 b.20 c.21 d.22 2. How many

Algebra ->  Finance -> SOLUTION: 1. If there are 7 points in a plane, no three of which are collinear, how many distinct lines can be formed by connecting two of those points> a. 18 b.20 c.21 d.22 2. How many      Log On


   



Question 1088488: 1. If there are 7 points in a plane, no three of which are collinear, how many distinct lines can be formed by connecting two of those points>
a. 18 b.20 c.21 d.22
2. How many combinations of three dishes can be prepared if you have the recipes for 10 dishes?

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
1. If there are 7 points in a plane, no three of which are collinear, how many distinct lines can be formed
by connecting two of those points ?

a. 18  
b. 20 
c. 21 
d. 22


You can draw one and only one straight line through each pair of these points.

Therefore, the answer is %287%2A6%29%2F2 = 7*3 = 21.

It is the number of combination of 7 items taken 2 at a time: C%5B7%5D%5E2 = 21.


On Combinations, see the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".