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