11.4. Permutations Where Repetitions Are Allowed

Try these first

1. 1.

   What is the formula for permutations with repetitions allowed?

   Hint

   Remember that n stands for the number of distinct items.

2. 2.

   How many permutations can be formed by selecting 2 letters from {A, B} with repetition?

   Hint

   Think about how many choices you have at each position.

3. 3.

   When repetitions are allowed, what is the number of permutations for arranging 3 items chosen from 4 distinct items?

   • 4
   • 12
   • 64

   Hint

   Think about how many options each position has.

4. 4.

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

   • True
   • False

   Hint

   Remember, combinations are about selecting groups.

5. 5.

   If a student can choose any number of fruits from 5 available types, how many combinations of 3 fruits can be made if repetitions are allowed?

   Hint

   Think about how you can represent this as choosing fruits where order does not matter.

6. 6.

   Imagine you're coding a simple game character. If you can select 3 powers from 6 distinct powers, but can select the same power multiple times, what would be the total power combinations?

   Hint

   Consider how many powers can occupy each slot!