I need an explanation how to do this ASAP I will give you 20 POINTS!! How many three-digit numbers can be formed using the digits 0 and 1? Repeated digits are allowed.

For the first digit you are choosing from 2 digits
for the second digit you are choosing from 2 digits
for the third digit you are choosing from 2 digits
2*2*2=8
111
110
011
101
000
001
100
010
However
A number doesn't usually start with a 0 or 0s.
Therefore, if you want 3-digit numbers and not just permutations using 0 and 1, then you must eliminate
011, 000, 001, and 010
Seeing that the first digit can't be 0, you choose from 1, then 2, and then 2 digits again; 1*2*2=4 numbers
You choose which answer best suits your problem.

About 15 inches- by pythag- \sqrt{16^{2} - 5^{2} }