2. You might like to refer to Example 6.5.5 on page 327 of the textbook.
The following table illustrates some solutions to the equation x + y + z = 11.
Categories for x, y and z |
Solution to the equation x + y + z = 11 |
| ×× | ××××××××× | | x = 2, y = 9, z = 0 |
| ×××× | ×××× | ××× | x = 4, y = 4, z = 3 |
| × | ××× | ××××××× | x = 1, y = 3, z = 7 |
The table demonstrates that the number of solutions to the equation x + y + z = 11 is the same as the number of arrangements of 11 crosses and 2 bars.