Exercise 3.

Each of the counting problems below can be solved with stars and bars. For each, say what outcome the diagram

\begin{equation*} ***|*||**| \end{equation*}

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 \(x_1 + x_2 + x_3 + x_4 = 6\text{.}\)

Solution.
in-context