Are my answers correct? Please help!! **Title: Understanding License Plate Combinations**Suppose that in a certain state, all automobile license plates have three uppercase letters followed by three digits. Use the method illustrated in Example 9.2.2 to answer the following questions.**(a) How many different license plates are possible?**To answer this question, think of creating a license plate as a 6-step process, where steps 1-3 are to choose the uppercase letters to put in positions 1-3 and the remaining steps are to choose the digits to put in the remaining positions. There are $17576$ ways to perform steps 1-3, and there are $1000$ ways to perform the remaining steps. Thus, the number of license plates is $17576000$.**(b) How many license plates could begin with A and end in 0?**In this case, the number of ways to place the A in Step 1 is $1$, and the number of ways to place the 0 in the final step is $1$. Thus, the answer is $676000$.**(c) How many license plates could begin with HV7?**In this case, the number of ways to perform steps 1-3 is $1$. Thus, the answer is $1000$.**(d) How many license plates are possible in which all the letters and digits are distinct?**$11232000$**(e) How many license plates could begin with AB and have all letters and digits distinct?**$17280$ **Example 9.2.2: Counting and Probability of PINs****Problem:**- **b.** How many different PINs are possible if repetition of symbols is not allowed?- **c.** What is the probability that a PIN does not have a repeated symbol assuming that all PINs are equally likely?**Solution:****a.** Some possible PINs are RCAE, 3387, B92B, and so forth. You can think of forming a PIN as a four-step operation where each step involves placing a symbol into one of four positions, as shown below.**Diagram Explanation:**- The pool of available symbols includes the alphabets A-Z and digits 0-9.- For each of the four positions (1, 2, 3, and 4), there are 36 choices.**Steps:**- **Step 1:** Choose a symbol to place in position 1.- **Step 2:** Choose a symbol to place in position 2.- **Step 3:** Choose a symbol to place in position 3.- **Step 4:** Choose a symbol to place in position 4.There are a fixed number of ways to perform each step, namely 36, regardless of how preceding steps were performed. By the multiplication rule: $36 \times 36 \times 36 \times 36 = 36^4 = 1,679,616$ PINs in all.**b.** Again, think of forming a PIN as a four-step operation: Choose the first symbol, then the second, then the third, and then the fourth. There are:- 36 ways to choose the first symbol,- 35 ways to choose the second,- 34 ways to choose the third,- 33 ways to choose the fourth.The multiplication rule can be applied: $36 \times 35 \times 34 \times 33 = 1,413,720$ different PINs with no repeated symbols.**c.** By part (b) there are 1,413,720 PINs with no repeated symbol, and by part (a) there are 1,679,616 PINs in all. Thus the probability that a PIN chosen at random contains no repeated symbol is $\frac{1,413,720}{1,679,616} = 0.8417$. This means

Answered: Image /qna-images/answer/85271b76-6da6-4dbd-9b70-6e2ae0a120ec.jpg

Suppose that in a certain state, all automobile license plates have three uppercase letters followed by three digits. Use the method illustrated in Example 9.2.2 to answer the following questions. (a) How many different license plates are possible? To answer this question, think of creating a license plate as a 6-step process, where steps 1-3 are to choose the uppercase letters to put in positions 1-3 and the remaining steps are to choose the digits to put in the remaining positions. There are 17576 ways to perform steps 1-3, and there are 1000 111ways to perform the remaining steps. Thus, the number of license plates is 17576000 (b) How many license plates could begin with A and end in 0? In this case, the number of ways to place the A in Step 1 is 1 and the number of ways to place the 0 in the final step is 1 Thus, the answer is 67600 (c) How many license plates could begin with HVI? In this case, the number of ways to perform steps 1-3 is 1 Thus, the answer is 1000 (d) How many license plates are possible in which all the letters and digits are distinct? 11232000 (e) How many license plates could begin with AB and have all letters and digits distinct? 17260

Suppose that in a certain state, all automobile license plates have three uppercase letters followed by three digits. Use the method illustrated in Example 9.2.2 to answer the following questions. (a) How many different license plates are possible? To answer this question, think of creating a license plate as a 6-step process, where steps 1-3 are to choose the uppercase letters to put in positions 1-3 and the remaining steps are to choose the digits to put in the remaining positions. There are 17576 ways to perform steps 1-3, and there are 1000 111ways to perform the remaining steps. Thus, the number of license plates is 17576000 (b) How many license plates could begin with A and end in 0? In this case, the number of ways to place the A in Step 1 is 1 and the number of ways to place the 0 in the final step is 1 Thus, the answer is 67600 (c) How many license plates could begin with HVI? In this case, the number of ways to perform steps 1-3 is 1 Thus, the answer is 1000 (d) How many license plates are possible in which all the letters and digits are distinct? 11232000 (e) How many license plates could begin with AB and have all letters and digits distinct? 17260

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: I am seeing different answers for the same question, can you do it again properly and precisouly

A: This is the correct way of solving and solution

Q: Are you sure this is right

A: Yes, the solution given is correct.

Q: 2- Research always has some limitations and some flaws, and our findings are always subject to

A: Research is a deep study or extra study about the topic. Since it is research, the person should…

Q: Hello, you did not clear up my confusion in the question and the answer you put does not match the…

A: Any point in the polar coordinate system is represented by the point: r, θ. The polar form of the…

Q: Find the equation of the line that passes tru the points (-1,-3) and (5,1)

A: Given points are: (-1,-3) and (5,1) Equation of line: y-y1=m(x-x1) Where (x1,y1)=(5,1) m=slope of…

Q: 3. Consider the definite integral 8 V16 + 6x – x²dx. a) Estimate I by partitioning the interval…

Q: art b is wrong

A: The mean and standard deviation for difference is 12.35 and 59.89 respectively.

Q: part c is wrong. please fix that!!

A: s=23.90 n=16

Q: The selling price per unit of a product is $30, the fixed costs per month are $12,500, and the total…

Q: can this be done by a human?

A: F(s)=(-4s-2) /(s2-2s+26)

Q: kpression for "12 times x."

A: Times means multiplication. Sometimes it is denoted by dot.

Q: This is the wrong answer！！！

Q: I am trying to help my son with a few of these questions and I am lost. Any help is appreciated.

A: Let a cuboid has Length l, width w and height h, then- Volume of cuboid = lwh Surface area of cuboid…

Q: Part C is incorrect, please help! So, that will probably mean parts D and E are also incorrect.

A: In the given problem, a one-proportion z-test was conducted to test the claim whether a drug caused…

Q: Please help with these questions and show work need it asap!!! Thank you

A: The frequency distribution of the data set represents the class intervals and corresponding…

Q: Is it true or false?

Q: I'm having a really hard time with this problem. Please help!!

Q: What is useful denial of" all cockroaches can fly".

Q: It says b is wrong. first part was right. second was wrong

Q: It is wrong. It says they are both incorrect.

A: X-intercepts are found by substituting y=0 in the given function.

Q: it is wrong, can you try doing it again?

A: We have to find the particular solution for the given differential equation.

Question

Are my answers correct? Please help!!

**Title: Understanding License Plate Combinations**

Suppose that in a certain state, all automobile license plates have three uppercase letters followed by three digits. Use the method illustrated in Example 9.2.2 to answer the following questions.

**(a) How many different license plates are possible?**

To answer this question, think of creating a license plate as a 6-step process, where steps 1-3 are to choose the uppercase letters to put in positions 1-3 and the remaining steps are to choose the digits to put in the remaining positions. There are $17576$ ways to perform steps 1-3, and there are $1000$ ways to perform the remaining steps. Thus, the number of license plates is $17576000$.

**(b) How many license plates could begin with A and end in 0?**

In this case, the number of ways to place the A in Step 1 is $1$, and the number of ways to place the 0 in the final step is $1$. Thus, the answer is $676000$.

**(c) How many license plates could begin with HV7?**

In this case, the number of ways to perform steps 1-3 is $1$. Thus, the answer is $1000$.

**(d) How many license plates are possible in which all the letters and digits are distinct?**

$11232000$

**(e) How many license plates could begin with AB and have all letters and digits distinct?**

$17280$

**Example 9.2.2: Counting and Probability of PINs**

**Problem:**
- **b.** How many different PINs are possible if repetition of symbols is not allowed?
- **c.** What is the probability that a PIN does not have a repeated symbol assuming that all PINs are equally likely?

**Solution:**

**a.** Some possible PINs are RCAE, 3387, B92B, and so forth. You can think of forming a PIN as a four-step operation where each step involves placing a symbol into one of four positions, as shown below.

**Diagram Explanation:**
- The pool of available symbols includes the alphabets A-Z and digits 0-9.
- For each of the four positions (1, 2, 3, and 4), there are 36 choices.

**Steps:**
- **Step 1:** Choose a symbol to place in position 1.
- **Step 2:** Choose a symbol to place in position 2.
- **Step 3:** Choose a symbol to place in position 3.
- **Step 4:** Choose a symbol to place in position 4.

There are a fixed number of ways to perform each step, namely 36, regardless of how preceding steps were performed. By the multiplication rule: $36 \times 36 \times 36 \times 36 = 36^4 = 1,679,616$ PINs in all.

**b.** Again, think of forming a PIN as a four-step operation: Choose the first symbol, then the second, then the third, and then the fourth. There are:
- 36 ways to choose the first symbol,
- 35 ways to choose the second,
- 34 ways to choose the third,
- 33 ways to choose the fourth.

The multiplication rule can be applied: $36 \times 35 \times 34 \times 33 = 1,413,720$ different PINs with no repeated symbols.

**c.** By part (b) there are 1,413,720 PINs with no repeated symbol, and by part (a) there are 1,679,616 PINs in all. Thus the probability that a PIN chosen at random contains no repeated symbol is $\frac{1,413,720}{1,679,616} = 0.8417$. This means

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

It is not well explained i am confused
problem is attached! i am completly stucked. please help. please review both attachments before answering . thank you so much!
It says it is incorrect. Do you have other way?
but the answer in the book said test doesn't apply?
What is Power and Multiple Rules?
How is this wrong? Please help!
Is this the solution to the question posted or this is an error ?
One is neither positive nor negative true or false