Question

In a state 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 the calculations for this lottery involve the combinations rule or either of the two permutations​ rules? Why or why​ not? If​ not, what rule does​ apply?

Answer 1

See explanation below

Explanation:

The calculations for this lottery do not involve the combinations rule because the order of the numbers does matter. For example, 1234 and 4321 are different although they have the same digits.

The calculations for this lottery do involve the permutations with replacement rule because any selected number can be used more than once.

By the fundamental rule of counting, there are 10*10*10*10 = 10,000 possible outcomes of the event with a probability 1/10,000 = 0.0001 each outcome.