**Instructions:** Except for questions that ask for a simple True or False, complete solutions with details are required with reasons for each of the operations you perform to obtain a solution. For example, if the problem asks for a *Proof*then we need to see all the steps of the argument as is given in your eResource textbook. (Discrete Structures

- Prove that if 51 positive integers between 11 and 100 are chosen, then one of them must divide another.
- How many distinct permutations are there of the characters in the word MONGOOSES?
- Given a computer network with 60 switching nodes. In how many ways can one or two nodes fail?
- Given a computer network with 60 switching nodes. If one node has failed, in how many ways can seven nodes be selected without encountering the failed node?
- A cheese shop carries a large stock of 34 kinds of cheese. By the end of the day, 48 sales have been made, and the items sold must be restocked. How many different restocking orders are possible?
- Explain why C(n, n-1) = C(n, 1).
- In 5-card poker a hand is 5 cards dealt from a standard 52-card deck. How many hands contain two pairs (that is two pairs of different kinds plus a fifth card of some third kind.)?
- How many distinct non-negative integer solutions are there to the equation

x _{1}+x_{2}+ x_{3}+ x_{4}= 10 - In how many different ways can you seat 11 men and 9 women in a row if the men all sit together and the women all sit together?

Subject | Mathematics |

Due By (Pacific Time) | 10/25/2014 12:00 pm |

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