5
votes
0answers
69 views

Finding the number of 5-node labeled connected graphs via generating functions

Problem: Find the number of ways to connect a graph having 5 labeled nodes so that each node is reachable from every other node. I have solved this problem using principle of inclusion and exclusion ...
0
votes
1answer
364 views

Number of 5 letter words over a 3 letter alphabet using each letter at least once

This is similar to my previous question, Number of 5 letter words over a 4 letter group using each letter at least once. The only difference is that there are 3 letters to choose from instead of 4. ...
2
votes
2answers
258 views

Inclusion Exclusion vs. Generating Functions

To what extent are the Inclusion Exclusion principle and Generating Functions interchangeable? Is there a general principle? For instance, I asked the following question, Number of 5 letter words ...