11.6. Unordered Selection of k Elements

Try these first

1. 1.

   How many ways can you choose 2 fruits from a basket of 4 different fruits?

   Hint

   Use the formula C(n, k) = n! / (k!(n - k)!)

2. 2.

   What is C(5, 0)?

   Hint

   Think about picking no items at all.

3. 3.

   What is the formula for combinations?

   • A) C(n
   • k) = n! / (k!(n - k)!)
   • B) P(n
   • k) = n! / (k!(n - k)!)
   • C) C(n
   • k) = k! / (n!(n - k)!)

   Hint

   Recall how we derive the number of ways to select.

4. 4.

   True or False: The order of selection matters in combinations.

   • True
   • False

   Hint

   Think about how you list selections to compare.

5. 5.

   Using a set of letters A, B, C, D, E, how many ways can you select 3 letters if repetitions are not allowed?

   Hint

   Remember the formula for choosing without replacement!

6. 6.

   In a flower shop with 6 types of flowers, how many distinct bouquets of 4 can be created allowing repetitions?

   Hint

   Think how grouping flowers allows flexibility in counts.