Discrete Mathematics Answers

Part I: Adjacency Matrix and Shortest Path

Construct a graph based on the adjacency matrix that appears below. Label all nodes with indices consistent with the placement of numbers within the matrix.

0 6 0 5 0
| 6 0 1 0 3 |
| 0 1 0 4 8 |
| 5 0 4 0 0 |
0 3 8 0 0

1) Describe the graph and why it is consistent with the matrix.
2) How many simple paths are there from vertex 1 to vertex 5? Explain.Which is the shortest of those paths?

There are 12 micro phones 8 laser printers in an office. Find the minimum number of connections to be made which will guarantee that if 8 or fewer computers want to print at the same time, each of them will be able to use a different printer.

There are 12 micro phones 8 laser printers in an office. Find the minimum number of connections to be made which will guarantee that if 8 or fewer computer want to print at the same time, each of them will be able to use a different printer.

In how many ways can a committee of 5 be formed from a group of 11 people consisting of 4 teachers and 7 students if
1. There is no restiriction in the selection?
2. The committee must include exactly 2 teachers?
3. The committee must include at least 3 teachers?
4. A particular teacher and a particular student cannot be both in the committee?

why Complete Bipartite edge =m.n and how can i proof it by use hanshaking lemma

what is combination?