Combinations/Permutations

Erik gets to choose from five cake flavors, seven icing flavors, and three topping flavors. If he can only choose one of each flavor,  how many cakes are possible?

• 35

• 573

• 21

• 105

Grant has five pairs of pants, nine shirts, and six ties. How many different outfits can he make consisting of one pair of pants, one shirt, and one tie?

• 45

• 270

• 30

• 54

Rylan’s basketball team has 11 players. How many ways can his coach choose five starting players?

• 462

• 55440

• 55

• 1000

Sarah plays softball over the summer.  If there are 10 players on the team, how many ways can the coach make a batting order that includes all players?

• 1
• 3628800
• 100
• 1814400

Permutation or Combination?

There are eight seniors on the football team that are being considered as team captains.

If there will be 3 team captains, how many different ways can 3 of these seniors be

chosen as captains?

• Permutation

• Combination

In a Permutation the order of the outcomes ​ ​ (a)   , but in a Combination the order​ (b)  

• matters

• doesn't matter

Ten students in your math class are presenting unique proofs to their classmates.  The order in which the proofs are chosen to be presented is random.   Find the probability that the proof using the HL Theorem is chosen first and your proof on CPCTC Theorem is chosen to go second.  

• 1/10

• 1/10!

• 4/5

• 1/90

How many ways can 8 runners finish in the top 3 places where the prizes for 1^st, 2^nd, and 3^rd are all different and matter?

Mathematical Equivalence

ON

The Nebraska license plate has 6 characters, each one filled with a number (0-9) or a letter. How many license plates are possible?

• 36

• 2176782336

• 60

• 1402410240

Calculate ₈P₂

Mathematical Equivalence

OFF