# Lesson Worksheet: Counting With Repetition Where Order Does Not Matter Mathematics

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

**Q1: **

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?

**Q2: **

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?

**Q3: **

How many integer solutions are there for the equation , given that , , and ?

**Q4: **

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

- A
- B
- C
- D
- E

**Q5: **

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?

**Q6: **

How many nonnegative integer solutions are there to the equation ?

**Q7: **

Mia 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?

**Q8: **

A boy is asked to select two flags for football clubs out of 4 different flags. In how many ways can such a selection be made if he can choose the same flag twice and the order of the two flags is not important?

**Q9: **

If you need to distribute 5 identical chocolate bars among 3 girls such that each girl takes at least one, in how many ways can you distribute the chocolate bars?

**Q10: **

You need to select three letters. The letters will be selected from a set of 4 letters. Repetition of letters is allowed and the order is not important.

How many such selections can be made?

- A4 selections
- B12 selections
- C24 selections
- D20 selections
- E3 selections