Solve the three counting problems below. Then say why it makes sense that they all have the same answer. That is, say how you can interpret them as each other.
How many ways are there to distribute 8 cookies to 3 kids?
How many solutions in non-negative integers are there to \(x+y+z = 8\text{?}\)
How many different packs of 8 crayons can you make using crayons that come in red, blue and yellow?