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Discrete structures

We worked on the attached problems today in class I am now trying to work through them again for understanding and I am not getting very far. My skills in discrete mathematics are not such that I can work through these on my own effectively.

3. Seven points are located in a plane. List the possible numbers of lines determined by these points. Your final answer is simply a list of whole numbers. You should indicate how each comes about.

4. Ten pieces of candy are distributed randomly to three children, Arlo, Burl, and Clovis.
a. What is the probability that Arlo gets no candy?
b. What is the probability that Arlo gets more candy than Burl and Clovis together?

5. In the grid below, we will be interested in the number of paths from point A to point B. A step in a path is either one move to the right or one move up (never moving away from B).


Solution Summary

There are three discrete problems here, regarding number of lines determined by points in a plain, probability of candy distribution, and the number of paths between points.