November+22+Combinatorics+Review

On tuesday we mainly reviewed the various ways to solve the combinatorics problems with "slots", such as making different numbers out of only 1's and 2's.

In the first example, we were trying to figure out how many 5 digit numbers could be made using only 1's and 2's. One way to look at this is that you have 5 slots (place values), and 2 options for each slot (1 or 2). Since you have 2 choices for each of five slots, the total number of possibilities would be media type="custom" key="11471282", or media type="custom" key="11471328". Another way you could think about this is in terms of choose notation. You would express this like media type="custom" key="11471354". The way to verbalize this idea is that you have 5 possible 1's, and you are choosing how many 1's you will have in your number.

For the rest of class we worked on problems from the book using the "box" method. The box method is when you think of the problem as being made up of boxes with certain items inside. You then have to figure out how many ways there are to put one item in each box.

HAPPY THANKSGIVING!