11.7. Combinations With Repetitions

Try these first

1. 1.

   How many ways can you choose 2 fruits from 3 types if repetitions are allowed?

   Hint

   Use the formula C(n+r-1, r)

2. 2.

   Calculate the combinations of selecting 4 candies from 2 types.

   Hint

   Think of 'bars' to separate candy types.

3. 3.

   What does combinations with repetitions mean?

   Hint

   Think about choosing items where order doesn’t matter, but you can select duplicates.

4. 4.

   True or False: In combinations with repetitions, the order of selection matters.

   • True
   • False

   Hint

   Recall that combinations focus on selection not arrangement.

5. 5.

   You need to select a committee of 4 from 3 distinct departments ensuring each department is represented. Calculate the possible setups.

   Hint

   Use the stars and bars method with the added representation of departments.

6. 6.

   In a garden, you want to plant 10 flowers using 3 types that can be repeated. How many arrangements are possible?

   Hint

   This is akin to distributing the flowers into types using combinations.