POW #3 - Code Lock Riddle

A safe has a code lock that unlocks if you input the correct three digit code, in any order. The lock has a keypad with the digits 0,1,2,3,4,5,6,7,8,9.

Problem Statement:

I can use three digit combinations with the digits 0,1,2,3,4,5,6,7,8,9 to find how many different unlock codes there are.

Process/Work:

Solution:

6000 ways to combine 3 digits using 10 numbers

Evaluation:

I think there are many ways to solve this problem. My answer is very exact and I think there could be more combinations possibly with so many numbers. But this made the most sense to me because you can rearrange all the 3 digit numbers into 6 combinations.

Problem Statement:

I can use three digit combinations with the digits 0,1,2,3,4,5,6,7,8,9 to find how many different unlock codes there are.

Process/Work:

- There are 6 ways to order 3 digits in a row. = 3x2x1
- Therefore: I want all possible three digit numbers
- If I want all possible three digit numbers, I have 10 choices for the first number
- I have 10 choices for the 2nd number, and 10 choices for the 3rd number giving you 10x10 = 1000 choices to arrange the 10 numbers.
- There are 6 ways to arrange each of these 1000 choices
- So: 1000x3x2x1
- This equals 6000

Solution:

6000 ways to combine 3 digits using 10 numbers

Evaluation:

I think there are many ways to solve this problem. My answer is very exact and I think there could be more combinations possibly with so many numbers. But this made the most sense to me because you can rearrange all the 3 digit numbers into 6 combinations.