Sometimes the objects in a group cannot be distinguised.  For example, think of a group of scrabble tiles: "ALBAASR".  An ordered arrangement of these 7 letters will have fewer combinations than 7 different scrabble tiles, because we cannot distinguish the difference between the different A's.  We could have a different situation where we need to put certain items together, or keep certain items apart.  These introduce further constraints.  In both of these cases, we need to find out the total number of permutations, which will be different than if all of the symbols are unique

Resources:

• Notes

Assignment:

• p524 #9-11, 14, 16-21, 25 *29, 32

Things you should be able to do after today:

• determine the number of permutations in a group if all the letters are used and there are repetitions within the group
• determine the number of permutations in a group if all of the members are used and there are constraints on the positions of those symbols
• apply the fundamental counting principle to problems that involve two different groups