Permutations and Combinations to Determine Probabilities of Compound Events

Rylan’s basketball team has 11 players. How many ways can his coach choose five starting players? Positions do not matter

• 462

• 55440

• 55

• 1000

Ashlyn needs to bring a dessert to her dinner party. If the bakery has eight pies to choose from, how many ways can Ashlyn choose three?

• 336

• 56

• 24

• 100

If Lucas owns 11 hoodies, how many ways can he choose four to bring on vacation?

• 44

• 7920

• 330

• 121

There are 18 people running in a cross country race. How many possible ways are there to place the runners in first, second, and third?

• 324

• 4896

• 816

• 54

A disc jockey has to choose three songs for the last few minutes of his evening show.  If there are nine songs that he feels are appropriate for that time slot, then how many ways can he choose and arrange to play three of those nine songs?

• 84

• 504

• 9!

• 3!

The ski club with ten members is to choose three officers for captain, co-captain and secretary.  How many ways can those offices be filled?

• 720

• 120

• 10!

A group of 25 people are going to run a race. The top 8 finishers advance to finals. How many different combinations can there be?

• 625

• 4.36 X 10¹⁰

• 1,081,575

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.

• 3 x 10¹²

• 120

• 3003

• 360,360