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Chapter 4: Q2 (page 174)

New Jersey Pick 6 In the New Jersey Pick 6 lottery game, a bettor selects six different numbers, each between 1 and 49. Winning the top prize requires that the selected numbers match those that are drawn, but the order does not matter. Do calculations for winning this lottery involve permutations or combinations? Why?

Short Answer

Expert verified

The calculation for winning the lottery involves combinations, as the order of the numbers does not matter.

Step by step solution

01

Given information

Six different numbers from 1 to 49 are selected in any order.

The lottery is won if the selected numbers match the numbers drawn, and order does not matter.

02

Differentiate between combination and permutation

Combination: The formula of combination is applied if only a certain number of items are to be selected from a pool without replacementsuch that order does not matter.

Permutation: The formula of permutation is applied if a certain number of items are to be selected from a pool without replacementsuch that order matters.

03

Identification for the given problem

It is given that six numbers are selected from 1 to 49 in any order and are then matched with the numbers of the lottery ticket.

As the order does not matter, the calculations involve combinations.

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