Decide whether each scenario should be counted using permutations or combinations. Explain your reasoning.

(a) Number of ways 10 people can line up in a row for concert tickets

(b) Number of different arrangements of three types of flowers from an array of 20 types

(c) Number of three-digit pin numbers for a debit card

(d) Number of two-scoop ice cream cones created from 31 different flavors

Question

Gunner

Mathematics

21 December, 03:16

Decide whether each scenario should be counted using permutations or combinations. Explain your reasoning.

(a) Number of ways 10 people can line up in a row for concert tickets

(b) Number of different arrangements of three types of flowers from an array of 20 types

(c) Number of three-digit pin numbers for a debit card

(d) Number of two-scoop ice cream cones created from 31 different flavors

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Answers (1)

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Carroll · Answer 1

a) Permutations. Order is important

b) Combinations. Order is not important.

c) Permutations. Order is important.

d) Combinations. Order is not important.

Step-by-step explanation:

When we use permutations and when we use combinations?

Permutations:

The order is important.

For example, a duo of Tremaine and Tre'davious is a different duo than Tre'davious and Tremaine.

Combinations:

The order is not important.

For example, a duo of Tremaine and Tre'davious is the same duo as Tre'davious and Tremaine.

(a) Number of ways 10 people can line up in a row for concert tickets

For example, suppose the starting grid for a Formula 1 race.

Charles LeClerc in first and Lewis Hamilton is second if a different formation than Lewis Hamilton in first and Charles LeClerc in second. So the order is important. The people lining up here follow the same logic.

This means that this is counted using the permutations formula.

(b) Number of different arrangements of three types of flowers from an array of 20 types

An arrangment of Roses, Violets and sunflower is the same as violets, roses an sunflowers, meaning that the order is not important.

So this is counted using the combination formula.

(c) Number of three-digit pin numbers for a debit card

A pin number of 123 is different than a pin number of 213, which means that the order is important.

So this scenario is counted using the permutations formula.

(d) Number of two-scoop ice cream cones created from 31 different flavors

Selecting a cone of cookie ice cream and then a cone of chocolate ice cream is the same as selecting a cone of chocolate ice cream and then a cone of cookie ice cream. This means that the order is not important.

So this scenario is counted using the combinations formula.