How many 7 digit numbers can be formed by the digits 1 2 3 4?

Answer 1

This is a problem called a permuation (if order matters).

For the first digit, you have 4 choices, for the second, you also have 4 choices:

So, if it were a two digit number, you would have 16 choices:

11 21 31 41

12 22 32 42

13 23 33 43

14 24 34 44

Notice that 16 is 4 x 4. This pattern can be generalized to get the following formula (Fundamental counting prinicple):

You multiply the number of choices for each slot to get the total number of arrangements:

So, for your question, it is 4 x 4 x 4 x 4 x 4 x 4 x 4= 16384.