1. The document discusses Prof. Irish's wardrobe options and uses a tree diagram to calculate the number of possible combinations of clothing he can wear before needing to repeat an outfit. 2. It is determined that with 4 pants, 3 shirts, 2 vests, and 4 ties, Prof. Irish has 96 possible outfits before repeating, allowing him to dress differently every day of the semester. 3. The document asks how many combinations would be possible if Prof. Irish had a second pair of shoes and provides examples of calculating combinations for other clothing quantities.

1. Do I need a full closet? Using tree diagrams to show multiple outcomes

5. Using a tree diagram Gray Tan Blue Black Each of the pants choices are listed, Each pair of pants can be matched with one of three colors of shirt: Red, brown, white

6. Setting up a tree diagram Gray Tan Blue Black Red Brown White Red Brown White Red Brown White Red Brown White Notice that if there are three choices for each of the pants there will be 4x3 or 12 different combinations.

7. 4 x 3 x 2 x ? Each of the twelve groups now can be paired with one of two vests. Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan We can now Add attach 4 ties to each Of the third list (vests) Gray Tan Blue Black Red Brown White Red Brown White Red Brown White Red Brown White

8. How many combinations can be made? Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Gray Tan Blue Black Red Brown White Red Brown White Red Brown White Red Brown White bb td ys tl

9. How many combinations can be made? Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan Blue Tan BB TD YS TxL Gray Tan Blue Black Red Brown White Red Brown White Red Brown White Red Brown White bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl bb td ys tl