Permutations and Combinations

How many ways can you arrange 2 letters from the word
S Q U A R E?

• 30
• 140
• 320
• 45

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

Your history teacher randomly chooses 2 out of 18 students to give an impromptu debate on freedom of press in the high school news paper.  What is the probability that both you and your best friend are chosen to give the debate?  

• 1/153
• 1/306
• 2/153
• 40/51

When does the order in which you are choose matter?

• Combination
• Permutation

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

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

• Permutation
• Combination
• Neither

Ambry must submit 4 paintings as part of her
application to art school. If she has 25 to choose from, how many ways can she pick 4?

• 12,650
• 303,600
• 100
• 254

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