There are 20 choices for the first number, 19 choices for the second number (since one number has already been chosen), and 18 choices for the third number. Therefore, the number of ways to choose three different numbers from 20 without repetition is:
20 × 19 × 18 = 6840
So there are 6840 different ways to choose a unique 3-number code.
A lock has a 3-number code made up of 20 numbers. If none of the numbers are allowed to repeat, how many different ways can you choose three different numbers in order for a unique code?
2 answers
There are 20 numbers to choose from for the first position, 19 for the second position, and 18 for the third position since we can't repeat any numbers. So the total number of unique codes is 20 * 19 * 18 = 6840.