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:
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
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.