Permutations and Combinations

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

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

• 15
• 40
• 80
• 10

How many 5-digit (numerical) passwords are possible for the school email system if the first digit cannot be 0?

• 11,424,400
• 10,967,424
• 9000
• 90,000

There are 6 roads from Ponder to Justin, 2 roads from Justin to Halslet, and 3 roads from Haslet to Saginaw.  How many possible routes are there from Ponder to Saginaw using only these roads and no backtracking? 

• 12
• 11
• 18
• 36

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