# How many 7 digit combinations can be made using the numbers 1 through 9?

It is: 9**C**7 = 36

### What are all different 4-digit combinations that can be made if using the numbers 0 through 9?

Multiple use of a digit. Using the numbers 0 through 9, all the numbers 0000 through 9999 can be made. That's 10,000 (ten thousand) numbers. There are 10 digits (0 through 9), and 10 x 10 x 10 x 10 = 10,000. The list would look like this: 0000, 0001, 0002, 0003, 0004, ..., 9995, 9996, 9997, 9998, 9999. Note that this list allows the repeated use of all the numbers. We're taking all the…

### If using numbers 0 through 9 how many different 3 digit combinations can be made?

There are 10 possible digits that can be used: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. If you can only use each digit once, there are 10 choices for the first digit, 9 remaining choices for the second digit, and 8 remaining choices for the final digit - 10 x 9 x 8 = 720 combinations. If you can use each digit repeatedly, you have 10 choices for each digit - 10…

### How many combinations of the numbers 1 and 4 can there be using four digits?

Think of either using or not using the numbers 1 and 4 for each digit. For example, let ____ ____ _____ ____ be the 4 digit number, now 1 can either go in to the first spot or 4 can. So there are 2 choices for that spot, and similarly two for the next spot and the next and the last. So there are 2^4 =16 combinations of 1 and 4 if we make 4…