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Selecting Coins How many different ways can you select one or more coins if you have 2 nickels, 1 dime, and 1 half-dollar?

11

Intro Stats / AP Statistics

Chapter 4

Probability and Counting Rules

Section 4

Counting Rules

Sampling and Data

Probability Topics

Missouri State University

University of North Carolina at Chapel Hill

Cairn University

Oregon State University

Lectures

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00:57

How many ways are there to…

01:20

These problems involve dis…

01:10

How many different combina…

00:54

These exercises involve di…

02:38

Consider a bag that contai…

02:37

$53-60$ Distinguishable Pe…

02:02

A penny, a nickel, a dime,…

Coin Toss How many differe…

03:26

In $32-37,$ determine the …

01:49

02:40

Ticket Selection How many …

00:37

Find the number of possibl…

00:30

In how many different ways…

00:28

Consider the following exp…

00:12

You pick a coin at random …

01:21

Coins You have 3.70 dollar…

00:40

02:03

Show that four coins can b…

00:47

In how many ways can a set…

02:17

You have 12 coins worth $\…

you have two nickels, one dime and one half dollar. And how many ways can we select one or more coins? Let's look at some characteristics of this problem. One characteristic is that as we select the coins, order is not important. Another characteristic is then two off the coins are identical. Let's look at some formulas that we can potentially use. So let's look at this formula combination and taken our. The assumption here is that we have in different objects. The juice from and order is not important, but in our problem, two of the objects took. The coins are identical, so we don't have four different objects, so we cannot use this formula about permutation. Rule number two. This formula here would you have n objects? Where are one are identical, arto are identical and so on. Now it's a permutation formula, which means order. It's important, so we cannot use that. In fact, the best way to solve this problem is just by listing all the different ways and then just counting the number of ways. So let's try doing that. So when we say one or more coins are to be selected and that means one coin for two coins or three coins or four points are selected. Let's let down the possibilities for each. Okay, now the ways to select one coin would be one nickel one time. Or you could select one half dollar. Note that the two nickels are identical, so they're indistinguishable. Ways to select two coins would be two nickels, one nickel, one dime, one nickel one have dollar, one dying, one half dollar ways to select three coins would be do a nickel one time do nickel one half dollar, one nickel, one dime, one half dollar. There's only one way to select all four points. Do Nico one dime, one half dollar. So let's can't the number off wastes to select the coins one or more going suits. 1234567 89 10 11. So there are 11 ways to select one or more coins from two nickels, one dime and one half brother

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