Combinations or Permutations

Do NOT use a calculator.

(a)  

Answer explanation

This is a permutations problem, because order matters. 6 × 5 × 4 × 3 × 2 × 1 = 720.

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.

• Combination

• Permutation

You are allowed to use a calculator.

• 24

• 36

• 360

• 720

Answer explanation

This is a permutations problem, in which you are counting possible sequences of four out of six tasks. 6 × 5 × 4 × 3 = 360.

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.

• Combination

• Permutation

You are allowed to use a calculator.

• 3

• 6

• 9

• 12

Answer explanation

This is a permutations problem: the question asks you how many possible sequences of three types of flowers are possible. 3 × 2 × 1 = 6.

You are allowed to use a calculator.

• 24

• 40

• 540

• 5040

Answer explanation

This is a permutations problem, because you are told that the role of Bystander #1 is different from the role of Bystander #4. (Notice the phrase “specific roles” in the question.) Thus, order matters. The question is asking how many sequences of four are possible given ten people. 10 × 9 × 8 × 7 = 5040.

A group of 45 people are going to run a race. The top three runners earn gold, silver, and bronze medals.

• Combination

• Permutation

You are allowed to use a calculator.

• 18

• 20

• 120

• 720

Answer explanation

This is a combinations problem asking how many groups of three out of six are possible. Use a table or an organized list. So, the answer is 20

You are allowed to use a calculator.

• 18

• 20

• 120

• 720

Answer explanation

This is a permutations problem asking how many sequences of three out of six are possible. 6 × 5 × 4 = 120.

Malcolm has to choose 5 numbers for his password (from digits 0 to 9) and repeat digits are not possible. How many different arrangements of numbers could Malcolm choose?

• Combination

• Permutation