Permutations and Combinations

Sarah 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 last one two weeks. How many possibilities are there for their vacation?

• 14

• 35

• 210

• 294

You are setting the combination on a three-digit lock. You want to use the numbers 123 but don't care what order they are in. How many possible combinations are there?

• 2

• 3

• 4

• 6

How many ways can a coach choose 3 players out of a team of 17 softball players to refill the water cooler?

• 51

• 680

• 2,049

• 4,080

How many ways can a club of 10 students elect a president, vice president, secretary, and treasurer?

• 3,628

• 4,020

• 5,040

• 6,500

How many ways can an employer fill four jobs: Computer Programmer, Software Tester, Manager, and Systems Engineer, if they have 15 applicants?

• 13,076

• 25,420

• 30,610

• 32,760

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 are possible?

• 40,320

• 126,925

• 525,225

• 1,081,575

How many ways can a teacher choose 5 students out of 13 to ride in a car instead of the van?

• 1,097

• 1,287

• 2,942

• 3,722

A group of 45 students are going to run a race. The top 3 runners earn gold, silver, and bronze medals. How many possibilities are there for these medals?

• 14,190

• 28,700

• 85,140

• 170,900

Rylan’s basketball team has 11 players. How many ways can his coach choose five starting players?

• 462
• 55440
• 55
• 1000

Tags

CCSS.HSS.CP.B.9

Determine the number of 4-letter arrangements that can be made using the word RHOMBUS.

• 5040
• 35
• 28
• 840

Tags

CCSS.HSS.CP.B.9