Permutations and Combinations

In a class of 19 students, how many different ways can I choose 3 of them to help with mentoring younger students?

• 791

• 969

• 1,512

• 2,110

In a race of 10 runners, how many different ways can the top 3 runners place? There are different prizes for 1st, 2nd, and 3rd.

• 560

• 650

• 720

• 830

There are 121 houses in a new development. A local surveyor needs to ask 3 random houses how many occupants they have. How many different ways can the surveyor choose 3 houses from the development?

• 124,593

• 221,043

• 245,431

• 287,980

In a group of 150 individuals, two of them are going to be winners of a raffle. Both winners selected will win $100. How many ways can the two winners be selected?

• 11,175

• 12,150

• 13,500

• 14,225

The varsity baseball team has 15 players. How many ways can the team members elect a captain and co-captain?

• 200

• 210

• 220

• 230

You are opening your locker, and the lock involves numbers 1-20. How many different possible ways can you arrange three numbers, without having any repeats?

• 4280

• 5500

• 6370

• 6840

How many ways can you arrange three letters on a license plate if repeats are allowed?

• 12,500

• 15,600

• 16,900

• 18,200

You have a playlist of 100 songs, but you only need 4 of them. How many ways can you choose 4 songs from your playlist of 100?

• 3,921,225

• 4,426,123

• 5,631,841

• 6,332,571

There is a basketball team of 11 total players. The coach needs to choose 5 players to start today's game. How many ways can the coach do this?

• 143

• 272

• 389

• 462

A school district is hiring a principal, vice principal, and attendance secretary. There are 12 total applicants. How many different ways can three individuals be hired for these positions?

• 980

• 1320

• 1460

• 1700