Question

Oregon Pick 4 In the Oregon Pick 4 lottery game, a bettor selects four numbers between 0 and 9 and any selected number can be used more than once. Winning the top prize requires that the selected numbers match those and are drawn in the same order. Do calculations for this lottery involve the combinations rule or either of the two permutation rules presented in this section? Why or why not? If not, what rule does apply?

Short answer

The calculation for the given lottery involves selection with replacement. Thus, the combinations rule and permutation rule do not apply here.

The multiplication counting rule can be used to obtain the total number of outcomes equal to 10000.

Step-by-step solution

Given information

• Select four numbers from 0 to 9.
• Any number can be used more than once.
• The lottery is won if the selected numbers match the numbers drawn in the same order.

Criteria for combination and permutation

In either of the two stated techniques, the selection must be made without replacement.

Combination: Used to compute the number of ways a certain number of items can be selectedwithout replacementwithout any particular order.

Permutation: Used to compute the number of ways a certain number of items can be arranged in different order opted outwithout replacement.

Identification for the given problem

It is given that four numbers are selected from 0 to 9, and any number can be used more than once. This implies that sampling is done with replacement.

As sampling is done with replacement, the rules of combinations and permutations cannot be applied.

The multiplication rule can be applied to compute the total number of possible ways to select the four numbers from 0 to 9.

Apply multiplication rule

The number of digits between 0 to 9 is equal to 10.

As the numbers are replaced each time, the number of digits available for selection for each selection remains 10.

Thus, the total number of outcomes becomes

$10\times 10\times 10\times 10\times 10=10000$

Thus, the multiplication rule is applied to count the ways to select four numbers, 10000.