Permutations & Combinations Warm Up

Does this scenario represent a permutation or combination?

A team of 8 basketball players needs to choose a captain and co-captain.

• Permutation

• Combination

Does this scenario represent a permutation or combination?

Rob and Mary are planning trips to nine countries this year. There are 13 countries they would like to visit. They are deciding which countries to skip.

• Permutation

• Combination

Does this scenario represent a permutation or combination?

The batting order for seven players on a 12 person team.

• Permutation

• Combination

Does this scenario represent a permutation or combination?

There are 45 applicants for three Computer Programmer positions.

• Permutation

• Combination

Castel and Joe are planning trips to three countries this year. There are 7 countries they would like to visit. One trip will be one week long, another two days, and the other two weeks. Find the number of possibilities that they could take their trip.

• 210

• 35

• 5040

• 840

You are setting the combination on a three-digit lock. You want to use the numbers 1, 2, and 3 but don't care what order they are in. How many combinations can you choose from?

• 27

• 1

• 6

• 3

A group of 25 people are going to run a race. The top 8 finishers advance to the finals. How many different groups of 8 could advance?

• 3.85 x 10²⁰

• 1.55 x 10²⁵

• 4.36 x 10¹⁰

• 1,081,575

A team of 17 softball players needs to choose three players to refill the water cooler. How many different groups can refill the cooler?

• 680

• 4080

• 3.56 x 10¹⁴

• 560

5 out of 13 students will ride in a car instead of a van. How many different groups could ride in the car?

• 38

• 1287

• 154,440

• 6,227,020,800

The student body of 10 students wants to elect a president, vice president, and secretary. How many different possibilities are there for these positions?

• 720

• 120

• 3,628,800

• 604,800