Combinations, Permutations, Factorials

Determine whether the following scenarios are a permutation or a combination:

Selecting a lead and an understudy for a school play.

• Combination

• Permutation

In how many ways can 3 different vases be arranged on a tray?

• 3

• 9

• 6

• 12

How many ways can you arrange 2 letters from the word

S Q U A R E?

• 30

• 140

• 320

• 45

Homecoming has 7 candidates for King. How many ways can a King and a First Runner-up be chosen to form the Festival Court?

• 23

• 840

• 42

• 3,628,800

Student council has 24 members. In how many different ways can a president, vice-president, treasurer, historian, and secretary be selected?

• 5,100,480

• 0

• 42,504

• 5.17 x 10²¹

A team of 17 volleyball players needs to choose three players to refill the water cooler. How many different ways can the players be chosen?

• 3360

• 560

• 4080

• 680

Find the possibilities when a group of 15 people are going to run a race. The top 5 finishers advance to the finals.

• 1.3 x 10¹²

• 120

• 3003

• 360,360

Picking a team of three people out of a group of 10.

• Permutation

• Combination

Choosing 3 toppings for your sundae out of a list of 15.

• Permutation

• Combination

Picking a President, Vice-President, and Secretary from a group of 12.

• Permutation

• Combination