If a salesperson has gross sales of over $\$ 600,000$ in a year, then he or she is eligible to play the company's bonus game: A black box contains 3 one-dollar bills, 1 five-dollar bill and 1 twenty-dollar bill. Bills are drawn out of the box one at a time without replacement until a twenty-dollar bill is drawn. Then the game stops. The salesperson's bonus is 1,000 times the value of the bills drawn. Complete parts (A) through (C) below. (A) What is the probability of winning a $\$ 27,000$ bonus? (Type a decimal or a fraction. Simplify your answer.)

Step 1 ：To win a $27,000 bonus, the salesperson must draw all the bills before drawing the twenty-dollar bill. This means the salesperson must draw a one-dollar bill, another one-dollar bill, another one-dollar bill, and then the five-dollar bill, and finally the twenty-dollar bill. The order of the one-dollar bills doesn't matter, but the five-dollar bill must be drawn before the twenty-dollar bill.

Step 2 ：The total number of ways to draw the bills is \(5!\) (5 factorial), because there are 5 bills and we are drawing them one at a time without replacement.

Step 3 ：The number of ways to draw the bills in the order described above is \(3! * 2\), because there are 3 one-dollar bills and we don't care about their order, and there are 2 ways to draw the five-dollar bill and the twenty-dollar bill (five first, then twenty).

Step 4 ：So the probability of winning a $27,000 bonus is the number of ways to draw the bills in the order described above divided by the total number of ways to draw the bills.

Step 5 ：Calculate the total number of ways to draw the bills: \(5! = 120\)

Step 6 ：Calculate the number of ways to draw the bills in the order described above: \(3! * 2 = 12\)

Step 7 ：Calculate the probability: \(\frac{12}{120} = 0.1\)

Step 8 ：Final Answer: The probability of winning a $27,000 bonus is \(\boxed{0.1}\) or \(\boxed{\frac{1}{10}}\)