Worksheet: Counting With Repetition Where Order Does Not Matter

In this worksheet, we will learn how to use combinations to count with repetition where order does not matter.


A magician wants to hide 4 identical balls in 16 boxes. More than one ball can be placed in a box. In how many ways can the balls be hidden?


Three friends are in a tapas restaurant. They would like to order 6 dishes to share. There are 15 different options on the menu. Given that they can choose multiple dishes of the same type, how many different possible ways can they order 6 dishes to share?


Twenty passengers get on an airport shuttle. The shuttle route includes six hotels, and each passenger gets off the shuttle at his/her hotel. The driver records how many passengers leave the shuttle at each hotel. How many different possibilities exist?


How many nonnegative integer solutions are there to the equation π‘₯+π‘₯+π‘₯+π‘₯+π‘₯=40οŠͺ?


Amelia is buying an ice cream cone and is able to pick two scoops from four flavors: chocolate, banana, strawberry, and vanilla. How many different ways can she pick two scoops from the four flavors?


How many possible diagonals can be drawn in a regular 𝑛-gon?

  • A𝑛(π‘›βˆ’3)2
  • B𝑛(π‘›βˆ’1)2
  • C𝑛(π‘›βˆ’1)
  • D𝑛2
  • E𝑛(π‘›βˆ’3)


How many integer solutions are there for the equation π‘₯+π‘₯+π‘₯=30, given that π‘₯>βˆ’5, π‘₯β‰₯4, and π‘₯>3?

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