• Introduction to Stars and Bars Problem.
• Count the number of ways to distribute n identical objects into k non-identical boxes
• Count the number of ways to distribute n identical objects into k non-identical boxes with no boxes being empty.
• How many ways are there to reach (n, n) from (0, 0) using only right and down moves?

Exercises:

1. How many integer solutions are there to the equation x+y+z=8 for which x, y, z are all integers greater than -3 ?
2. Using the digits 2 through 8, find the number of different 5-digit numbers such that:
   1. Digits cannot be repeated and must be written in increasing order. For example, 23678 is okay, but 32678 is not.
   2. Digits can be repeated and must be written in non-decreasing order. For example, 24448 is okay, but 24484 is not.