Math 300

Groupwork

Combination Problems

Dr. Wilson

 

Each group is to appoint a scribe who will record all of the work of the group. At the end of the period, each group will turn in the document prepared by the scribe with the signatures of all the group members.

 

In many of these exercises, it will prove helpful to use the problem solving technique of solving simpler problems and looking for a pattern. Pasal's Triangle will be helpful.

 

1. 7 people take part in a panel discussion. Each person is to shake hands with all of the other participants at the beginning of the discussion. How many handshakes take place? List them all.

 

2. 8 points are arranged in a circle and each point is joined to each other point by a line. How many lines are needed?

 

3. Linda lives in a neighborhood where the streets either go North and South or East and West, forming rectangular blocks. All the streets go all the way through the neighborhood. Linda lives 3 blocks South and 4 blocks West of her school. She enjoys a little diversity in her life, and so she tries to take a different route to school each day. How many different routes can she take which involve moving only North or East?

 

4. A basketball team has 11 players on its roster. Only 5 players can be on the court at one time. How many different groups of 5 players can the team put on the floor?

 

5. In problem 2, assume that there is no point inside the circle where three of the line meet. How many points of intersection are there inside the circle?

 

6. The triangluar numbers are obtained by adding ujp consecutive whole numbers starting with one. List the first 10 triangular numbers.