1. Combinatorics
a. How many ways are there to arrange 6 different books on a shelf?
b. A team of 5 basketball players must be selected from a group of 10 players. How many different teams are possible?
c. How many different 5-card poker hands can be dealt from a standard deck of 52 cards?
2. Graph Theory
a. What is the shortest path from node A to node F in the following graph?
b. How many connected components are there in the following graph?
c. What is the chromatic number of the following graph?
3. Boolean Algebra
a. Simplify the following expression using Boolean algebra: (A AND NOT B) OR (B AND C) OR (A AND C)
b. Write the truth table for the following Boolean expression: (A OR B) AND (NOT A OR C)
c. What is the dual of the following Boolean expression? AB + C(AB + D)
(Note: The dual of a Boolean expression is obtained by interchanging AND and OR operations and replacing 0s with 1s and 1s with 0s)