Permutations help!~~~ it is due today!!!

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cajunchicla2

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Hi All!

I hope someone can help me. My sister is very sick and has a homework assignment due. She cannot do it and I don't have time to learn the math to figure it out myself. I ordinarily wouldn't ask but if anyone can provide answers to the following, I'd be grateful. Thanks in advance!

Many cars have keyless entry. To open the lock you may press a 5-digit code on a set of buttons like on figure 1 (Figure 1 illustration keypad is five buttons labeled 1-2, 3-4, 5-6, 7-8, 9-0). The code may include repeated digits like 11433, 55512.
A) How many different 5-digit codes can be made using 1-10 if repetition is permitted?
B) How many different ways are there of pressing the 5 buttons if repetition is allowed?
C) A burglar is going to press 5 buttons at random, with repetition allowed. Find the probability that the burglar hits the sequence to open the door.

Suppose that each button had only one number associated with it as (1, 2, 3, 4, 5).
D) How many different 5 digit codes can be made with the 5 digits if repetition is permitted?
E) Using the buttons labeled 1-5, how many different ways are there to press 5 buttons if repetition allowed.
F) A burglar is going to press 5 buttons. Find the probability that the burglar hits the sequence to open the door.
G) Is a burglar more likely, less likely, or does he or she have the same likelihood of pressing 5 buttons and opening the car door if the buttons are labeled as in the first illustration (five buttons labeled 1-2, 3-4, 5-6, 7-8, 9-0) or as in the second illustration (five buttons labeled 1,2,3,4,5)? Explain
H) Can you see any advantages in labeling the buttons as in the first illustration?

Figure 1 illustration keypad
1-2, 3-4, 5-6, 7-8, 9-0

Figure 2 illustration keypad
1,2,3,4,5
 
cajunchicla2 said:
Hi All!

I hope someone can help me. My sister is very sick and has a homework assignment due. She cannot do it and I don't have time to learn the math to figure it out myself. I ordinarily wouldn't ask but if anyone can provide answers to the following, I'd be grateful. Thanks in advance!

Many cars have keyless entry. To open the lock you may press a 5-digit code on a set of buttons like on figure 1 (Figure 1 illustration keypad is five buttons labeled 1-2, 3-4, 5-6, 7-8, 9-0). The code may include repeated digits like 11433, 55512.
A) How many different 5-digit codes can be made using 1-10 if repetition is permitted?
B) How many different ways are there of pressing the 5 buttons if repetition is allowed?
C) A burglar is going to press 5 buttons at random, with repetition allowed. Find the probability that the burglar hits the sequence to open the door.

Suppose that each button had only one number associated with it as (1, 2, 3, 4, 5).
D) How many different 5 digit codes can be made with the 5 digits if repetition is permitted?
E) Using the buttons labeled 1-5, how many different ways are there to press 5 buttons if repetition allowed.
F) A burglar is going to press 5 buttons. Find the probability that the burglar hits the sequence to open the door.
G) Is a burglar more likely, less likely, or does he or she have the same likelihood of pressing 5 buttons and opening the car door if the buttons are labeled as in the first illustration (five buttons labeled 1-2, 3-4, 5-6, 7-8, 9-0) or as in the second illustration (five buttons labeled 1,2,3,4,5)? Explain
H) Can you see any advantages in labeling the buttons as in the first illustration?

Figure 1 illustration keypad
1-2, 3-4, 5-6, 7-8, 9-0

Figure 2 illustration keypad
1,2,3,4,5
Click to expand...

Please share your work, indicating exactly where you are stuck - so that we may know where to begin to help you.
 
What you have there is problems pertaining to permutations and combinations. Permutations are the ones that let you repeat numbers in the combos, whereas Combinations do not. So with that said...

Permutations:

Figure out how many "slots" to make for your first question 1A...meaning how many times a random thing must be chosen in this part of the problem, like for instance, a single number. Now look at the first thing that has to be picked. How many possible things can come up? For instance, if you had to pick a random letter in the alphabet, the number of possible things would be 26, which is not the same as your first number. Figure this out and put it in the first slot. Now repeat this process for each time a random thing needs to be picked, and put that number in its slot....

When you have finished, you should have some numbers that look suprizingly the same...in fact, they should all be the same! Because you always had the same amount of things to choose from for each "slot", right? :) Now multiply all of those numbers together...and that is how many possible permutations there are!! It's the total number of combos that can possibly ever be chosen. (which means it is your answer...be sure that the problem allows for the same thing to be repeated in more than one slot...if not, it is NOT a Permutation and your answer will be WRONG)

Combinations:

Very similar to Permutations, except things CAN NOT be repeated! The process is almost the same. Find out how many times something needs to be chosen (your number of "slots"). Find out the number of possiblities for the first choice or "slot". Record your answer. Now, things change. Again, a random letter yields 26 possiblities...What if I choose my first letter to be A? My second letter must not be A, because things can not be repeated. So I now have only 25 choices (one less!). Therefore 25 is the correct number for slot #2! Of course my 3rd choice could only be 24 different things (can't be A or B), right? Notice that again there is a pattern...each number is one less than the one before it (because each time you had to choose, there was one less thing to choose from). Multiply the numbers together, and this is your answer. This represents the number of choices when numbers aren't allowed to repeat.

Apply each part of your problem to 1 of these 2 strategys. Reply if probs.
 
So, I have been working at it with a little help and can you tell me if im right or way off.....
1) Since there are 10 digits, there are 10^5 different 5-digit codes.

2) Since there are 5 buttons, there are 5^5 different 5-digit codes using the buttons.

3) This is 5^5 / 10^5 = 1/2^5 = 1/32.
Alternately, each button contains 2 digits, so there are 2^5 ways to key a 5-digit code using the button.
==> The probability of 'accidentally' pressing the right code is 1 / 2^5.

4,5) There are 5^5 ways. (note the buttons represent distinct digits!)

6) This time, the probability is 1/5^5.

7) Since 1/2^5 > 1/5^5, he is more likely to open the door using the buttons as in Figure 1.

8) If there is any advantage, this figure is more forgiving if you're slightly off on your password.
(Of course, this is also to the burglar's advantage.)
 
Good job in seeing that every problem has to do with permutations. Check you answer for problem 3...you may want to review the logic you used for problem 6 to help you with that.

I will also advise you to check to make sure there are no other problems that count on the correct answer to problem 3.

Otherwise, you seem to be getting it. If you look up the equations for permutations and combinations (they look like nCr and nPr; the other variables n and r are also easily explained), they are both very useful and powerful tools for figuring out a wide range of problems pertaining to probability.
 
Can you elaborate... I don't understand where I messed up or where more answer needs to be given?!?! Please help it is due in a couple of hours!
 
cajunchicla2 said:
Hi All!

I hope someone can help me. My sister is very sick and has a homework assignment due. She cannot do it and I don't have time to learn the math to figure it out myself. I ordinarily wouldn't ask but if anyone can provide answers to the following, I'd be grateful. Thanks in advance!

Many cars have keyless entry. To open the lock you may press a 5-digit code on a set of buttons like on figure 1 (Figure 1 illustration keypad is five buttons labeled 1-2, 3-4, 5-6, 7-8, 9-0). The code may include repeated digits like 11433, 55512.

If I wanted to punch in 11357 or 12357 or 21357 or 22357 - would I punch in the same button sequence?

Is a number like 00357 permitted?

A) How many different 5-digit codes can be made using 1-10 if repetition is permitted?
B) How many different ways are there of pressing the 5 buttons if repetition is allowed?
C) A burglar is going to press 5 buttons at random, with repetition allowed. Find the probability that the burglar hits the sequence to open the door.

Suppose that each button had only one number associated with it as (1, 2, 3, 4, 5).
D) How many different 5 digit codes can be made with the 5 digits if repetition is permitted?
E) Using the buttons labeled 1-5, how many different ways are there to press 5 buttons if repetition allowed.
F) A burglar is going to press 5 buttons. Find the probability that the burglar hits the sequence to open the door.
G) Is a burglar more likely, less likely, or does he or she have the same likelihood of pressing 5 buttons and opening the car door if the buttons are labeled as in the first illustration (five buttons labeled 1-2, 3-4, 5-6, 7-8, 9-0) or as in the second illustration (five buttons labeled 1,2,3,4,5)? Explain
H) Can you see any advantages in labeling the buttons as in the first illustration?

Figure 1 illustration keypad
1-2, 3-4, 5-6, 7-8, 9-0

Figure 2 illustration keypad
1,2,3,4,5
Click to expand...
 
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