How many combinations are there for a 3 digit lock?

How many combinations are there if there are seven numbers and you have to have a four number combination?

That dependsThat depends upon whether you are allowed to repeat numbers. If you are allowed to repeat, that means that all seven digits (say 1 through 7) can be used in each of the four positions of your combination, even if a digit has been used in another position. That means there are 7 x 7 x 7 x 7 = 74 = 2401 possible combinations for your lock. But if you are not allowed to repeat, that means that every time you pick a digit for one spot, there will be one less digit for the next, and one less for the next, and so on. So, the first number can have seven possibilities, the second can have six, the third can have five, and the last can have four possible digits. That means there are 7 x 6 x 5 x 4 = 840 possible combinations for your lock, only about a third as many.Check out the related link at MathsIsFun. It has very good information on this subject.* * * * *That is true for PERMUTATIONS, but not for combinations. In a combination, the order of digits does not matter so that 1234 is the same as 1342 or 4213 ext.As a result you have 7C4 = 7!/[4!*(7-4)!] = 7*6*5/(3*2*1) = 35 combinations - not 2401.Incidentally, nCr is the notation for the number of combinations of r objects taken from n objects - exactly what the question asked for.

Original question

You can choose any of the 5 numbers as your first digit (5 options). For your second digit, you can also choose any of the 5 because repetitions are allowed. This gives $5\cdot5$ possibilities. Add in a third digit, once again choosing from the 5 numbers, and you have $5\cdot5\cdot5$, or 125, possibilities.

Question with limitations

Consider two cases. In one case, the first two digits are different. There are $5\cdot4$ possibilities that satisfy this. The third can be any of the 5, so there are $5\cdot4\cdot5=100$ possibilities for the first case.

In the second case, the first two digits are the same. There are $5\cdot1=5$ ways this can occur. In this case, the third digit must be different, giving you only 4 options to chose from. This means the second case has $5\cdot1\cdot4=20$ possibilities. Adding together the two cases, there are 120 possibilities.

An alternate way of thinking about the problem with limitations is to work backwards from the problem with no limitations. We have 125 possibilities before introducing limitations. Of those possibilities, there are only 5 that violate the limitations (111, 222, 333, 444, and 555). $125-5=120$, so there are 120 possibilities.

Want to figure out how to open a 3 digit combination lock box? If it’s a new lock box, set the code 0-0-0 by centering the digits in the lock. If you already have your new combination, set your current code in the center of the lock box. Move the locking lever from A to B.

Having a lock box for the first time may be exciting; however, opening it may cause confusion. With this tutorial, you don’t have to guess how to unlock a 3 dial combination lock. You can finish the task immediately if you follow the steps correctly.

Table of Contents

• What You Need
  • Combination Code
• What to do
  • Set your factory code or current combination number
  • Move the locking lever from A to B
• How Will I Open My Lock Box if I Forgot the Code
• How Many Possible Combinations Are There in a 3-digit Combination Lock
• Conclusion

What You Need

A 3 number combination lock is easy to open as long as you have the right kind of items. Fortunately, you will only need one item for this tutorial. However, this item is very necessary for you to open your lock.

Combination Code

If you haven’t set your code yet, you will need your factory code to unlock a 3 digit lock. Most of the factory codes for the new locks are 0-0-0. However, if this is not the case for you, you have to look for your factory code in the manual of the lock or on the side of its box.

In case you already have set a new code, use it to open the lock box. If you have forgotten your new code, you have to open the lock box by picking it. It is very important to secure the code of your lock box, especially if it’s resettable since the manufacturer cannot provide you with your new code.

What to do

Set your factory code or current combination number

If you haven’t set your new code, your factory code is what you need. The common factory code for most locks is 0-0-0. If this is not the case for your lock, look for your factory code. Set your code by rotating the dials into three 0s or pressing them if the lock box is a keypad.

In case you already set your new code, dial your current combination code by rotating the three dials corresponding to the numbers of your code. They must be correctly aligned for the lock to open.

Move the locking lever from A to B

To successfully open a combination lock box, you have to locate the locking lever. It is usually at the bottom of the lock box. Just push it from point A to point B. Once done, the lock box will automatically open. If you want to learn more, you can also check this video on opening & closing the MasterLock Lockbox.

How Will I Open My Lock Box if I Forgot the Code

You can crack a 3 wheel combination lock box by using two paper clips where one acts as the lock pick while the other one is the tension tool. Just move the pins using the picking tools until you have successfully pushed them upward. The lock will automatically open once the pins are in the unlocked position.

How Many Possible Combinations Are There in a 3-digit Combination Lock

There are possibly 1,000 combinations on a 3-digit combination lock. This kind of lock is secure to use because the codes are not easy to figure out. The more digit a combination lock has, the higher the possible combinations are.

Conclusion

Have you figured out how to open a 3 digit combination lock box through this tutorial? It is a breeze to unlock a 3 dial combination lock if you have a clear guide on how to do it. This tutorial is easy to follow, and you won’t have to ask anyone to help you out.

If you have friends who are new to using a lock box, why don’t you share this tutorial with them? We also want to know your suggestions and ideas on how to open a 3 digit combination lock on luggage. Just leave a comment below.

I am the last member to join Revolar and might be just the luckiest to work with dedicated people like Teddy and John. Our team has established a process where my only job is writing the best content to deliver incredible ideas and guides.

How many combinations are there in a 3 digit code?