11.5. Combinations and Its Relation to Permutations

Try these first

1. 1.

   What is the permutation of 4 objects taken 2 at a time?

   Hint

   Use the formula P(n, r) = n! / (n - r)!

2. 2.

   How many ways can you choose 3 out of 5 fruits?

   Hint

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

3. 3.

   What is the formula for finding permutations?

   • P(n
   • r) = n! / (n - r)!
   • C(n
   • r) = n! / (r!(n - r)!)
   • Both are correct.

   Hint

   Consider how order affects the arrangements.

4. 4.

   In combinations, does order matter?

   • True
   • False

   Hint

   Think about selecting a group of items.

5. 5.

   If a sports team has 12 players and 5 can be selected to form a different lineup, how many different lineups can be created? Consider both order and team selections.

   Hint

   Focus on how to arrange those players, and remember order is important!

6. 6.

   How many ways can 10 different books be chosen to have a 3-book series mixture, allowing some to be repeated in combinations?

   Hint

   Remember to think of how the repetition changes the selection criteria!