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Quinto Lottery A lottery game called Quinto is played by choosing five numbers each, from 0 through 9. How many numbers are possible? Although repeats are allowed, how many numbers are possible if repeats are not allowed?

100,000; 30,240

Intro Stats / AP Statistics

Chapter 4

Probability and Counting Rules

Section 4

Counting Rules

Sampling and Data

Probability Topics

University of North Carolina at Chapel Hill

University of St. Thomas

Boston College

Lectures

0:00

00:25

To win the jackpot in a lo…

00:46

Five-digit Numbers How man…

00:52

How many four-digit numbe…

00:48

How many five-digit numbe…

01:59

Forming Numbers How many t…

00:41

Four-digit Numbers How man…

01:08

How many 5 -digit numbers …

01:23

How many three-digit numbe…

01:02

Use any or all of the meth…

00:42

02:19

00:56

Find the probability of ea…

00:49

Use an appropriate rule of…

01:47

How many 3 -digit numbers …

02:12

How many 3 -different digi…

00:24

Find the probability of wi…

00:38

Solve each problem.Pla…

00:47

Determine the number of po…

02:32

How many four-digit odd nu…

00:26

Solve each problem.Fan…

we are tasked with a question about the accounting principle and how it's applied to a quinto game. Now, in the Quinto game, you choose five numbers. These are single digit numbers. And if I wrote down all of the single digit numbers, you will see that there are 10 of them 678 and nine. So if we count them up, there are 10 single digit numbers one through nine and then zero is, well, 10 single digit numbers. Um, according to the counting principle, if we can rephrase our question such that we say the words and then then that is a good indicator, that we will multiply each of the potential options together. So in the Quinta game, I will choose one number and then another number and then another number and then another number and then another number. Now our first selection has a total of 10 possibilities, and our second selection has 10 possibilities. Each selection. I can choose any of the 10 numbers since I said and then I can do 10 times 10 times 10 times 10 times 10 10 possibilities and then 10 more possibilities and then 10 more possibilities and then 10 more possibilities and then 10 more possibilities. That gives me 10 to the fifth power possibilities, which is 100 1000 now. In the second part of the question, if we choose five digits again, but we're not allowed to repeat the digits well, in the first digit we can choose from any of the 10. But for our second digit, we've already chosen one of them. Let's say, for example, that we chose the number two Well, that means we can no longer choose the number two. And so there are nine other possibilities, and we can now, let's say, for example, we chose number six that time. That means that there are only eight more possibilities. And so this time, using the can't counting principle, we would choose from 10 digits and then nine possible digits and then eight possible digits and then seven possible digits and then six possible agents. So our answer is 10 times nine times eight time, seven time six, which is let me get my calculator out so I can calculate this 10 times nine times, eight times seven times six is 30,000 240 possible combinations. So to review with the counting principle, if you can reword your question so that you used the phrase and then that indicates that you will be multiplying.

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