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 be... click for more

Recursively Defined Sequence : Find the 2001st Term

A sequence is define recursively by A0 = A, and An+1 = An /1 + nAn. Determine A2001.

Probability : Selection Without Replacement, Combinations and a Probability Tree

Three letters from A, B, C, D, and E are selected one at a time (without replacement). a. What is the probability that they are selected in alphabetical order? b. What is the probability that they are selected in alphabetical order, if B is the first letter selected.

Probability : Selection Without Replacement

John randomly picks (without replacing) four marbles from a jar that contains 6 red and 4 blue marbles. Mary randomly picks three marbles from a jar that contains 3 red and 5 blue marbles. What is the probability that John picks more blue marbles than Mary?

A = {1,2,3} and B = {a,b,c}, and let f: A B

A = {1,2,3} and B = {a,b,c}, and let f: A -> B (a) Give an example of a one to one function from A to B. Briefly explain why your example is a 1-1 function. (b) How many one to one functions from A to B are there? Explain. (c) Define a function f^-1, for some function f from A to B. (d) Is the function g: Z -> Z defined by g(n) = [n/2] a one to one function? Explain.