Exercise 3

Each of the counting problems below can be solved with stars and bars. For each, say what outcome the diagram $$***|*||**|$$ represents, if there are the correct number of stars and bars for the problem. Otherwise, say why the diagram does not represent any outcome, and what a correct diagram would look like.

1. How many ways are there to select a handful of 6 jellybeans from a jar that contains 5 different flavors?

2. How many ways can you distribute 5 identical lollipops to 6 kids?

3. How many 6-letter words can you make using the 5 vowels in alphabetical order?

4. How many solutions are there to the equation $x_1 + x_2 + x_3 + x_4 = 6$.