A vending machine accepts nickels, dimes, and quarters. Exact change is needed to make a purchase. How many ways can a person with four nickels, three dimes, and two quarters make a 55-cent purchase from the machine? For this problem, treat all coins within a particular value as if they are the same. That is, do not count the number of ways that a single coin (a nickel, a dime, or a quarter) could be chosen.
There are ways to make the purchase.

Step 1 ：Consider the number of quarters that can be used. We can use 0, 1, or 2 quarters.

Step 2 ：If we use 0 quarters, we need to make up 55 cents with nickels and dimes. But we can't do this because the maximum we can make with four nickels and three dimes is 50 cents.

Step 3 ：If we use 1 quarter, we need to make up 30 cents with nickels and dimes. We can do this in two ways: three dimes or two dimes and two nickels.

Step 4 ：If we use 2 quarters, we need to make up 5 cents with nickels and dimes. We can do this in one way: one nickel.

Step 5 ：Check the results: \(1\) quarter, \(3\) dimes (\(25 + 10 + 10 + 10 = 55\)), \(1\) quarter, \(2\) dimes, \(2\) nickels (\(25 + 10 + 10 + 5 + 5 = 55\)), and \(2\) quarters, \(1\) nickel (\(25 + 25 + 5 = 55\)). All of these combinations add up to 55 cents.

Step 6 ：\(\boxed{3}\) ways to make a 55-cent purchase from the machine.