Permutations and Combinations

Permutation or Combination: The student body of 30 students wants to elect a president, vice president, secretary, and treasurer.

• permutation

• combination

Permutation or Combination: Rob and Micaela are planning trips to four countries this year. There are 5 countries they would like to visit. One trip will be one week long, another two days, another two weeks, and the other a month.

• permutation

• combination

Permutation or Combination: A group of 40 people are going to run a race. The top three runners earn gold, silver, and bronze medals.

• permutation

• combination

Permutation or Combination: A group of 14 people need to take an elevator to the top floor. They will go in groups of seven. They are deciding who will take the elevator on its second trip.

• permutation

• combination

solve the following permutation: Jacob and Eugene are planning trips to four countries this year. There are 14 countries they would like to visit. One trip will be one week long, another two days, another two weeks, and the other a month.

• 24024

• 20876

• 1001

• 4804

solve the following permutation: The batting order for ten players on a 12 person team.

• 239018325

• 239500800

• 238985815

• 66

solve the following combination: Amanda and Jimmy are planning trips to four countries this year. There are 8 countries they would like to visit. They are deciding which countries to skip.

• 70

• 45

• 280

• 260

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

• 462
• 55440
• 55
• 1000

There are 14 candy bars for sale. How many ways can Andy choose five of them?

• 240240
• 2002
• 87178291200
• 70

Erik gets to choose from five cake flavors, seven icing flavors, and three topping flavors. If he can only choose one of each flavor,  how many cakes are possible?

• 35
• 573
• 21
• 105