1. A door has a lock with a 5-digit keypad. To unlock the door, a person must enter a passcode consisting of three different digits, with each digit entered in the correct order. What is the probability that a randomly chosen passcode consisting of three different digits unlocks the door?

Question

1. A door has a lock with a 5-digit keypad. To unlock the door, a person must enter a passcode consisting of three different digits, with each digit entered in the correct order. What is the probability that a randomly chosen passcode consisting of three different digits unlocks the door?
I know that it should be 1/n, but I never seemed to figure out he n. How do you find the total number of possibilities for this probability question?

2.A cyclist travels away from his house at an average speed of 40 km per hour. He immediately returns to the house by the same route at an average speed of 60 km per hour. What is the cyclist's average speed for the round trip in km per hour?
How do I find it when it asks for "average speed"?

3. The average cost of b books in a customer's online shopping cart is $24. The average cost of d DVD's in the same customer's online shopping cart is $16. If the average cost of the b books and d DVD's is $19, what is the value of d/b?
This question just makes no sense, and confuses me for some reason.

4. If the average(arithmetic mean)of four different positive odd integers is 80, what is the greatest possible value of one of the integers?
How do I approach these questions?

Steve · Answer

#1. I can't see where any n comes in at all. The chance of guessing the 3 digits in order is 1/5 * 1/4 * 1/3

That is, since there are 5P3=60 ways of picking 3 digits, and only one is correct, that's 1/60 chance of getting it right.

#2
avg speed = totaldistance/totaltime
total distance = 2d
total time = d/40 + d/60
avg speed is thus

2d/(d/40+d/60) = 48 km/hr

#3
total cost of books: 24b
total cost of dvds: 16d
total average cost: (24b+16d)/(b+d) = 19
So,
24b+16d = 19b+19d
5b = 3d
d/b = 5/3

#4
the greatest value of the largest can be achieved when the other three have the smallest total.

The sum of all four numbers is 4*80 = 320.

So, if the smallest three numbers are 1,3,5 then that leaves 320-9=311 for the largest one.

Linda · Answer

For #1, what does 5P3 mean? What is the P? And so for these type of questions its always 1/total number choices, times 1/total number of choices minus 1, etc for however many digits sought after for the question?

Linda · Answer

For #3, average cost of b books is $24 means that one book is $24 right? That was the only part I didn't get.. maybe is the language issue for me.