<PRE><B>Question 1133648</B>
&lt;br&gt;
56.&lt;br&gt;
But my showing you the whole process for finding the answer doesn&#39;t do you any good if you want to learn anything from the problem.&lt;br&gt;
So I&#39;ll show you how you can go about finding the answer and let you see if you come up with the right answer doing the work yourself.&lt;br&gt;
The number of $1 bills must be a multiple of 5.  So break the problem into cases for the different possible numbers of $1 bills:&lt;br&gt;&lt;pre&gt;
if there are 0 $1 bills, the amount remaining is $50; the number of ways to make $50 using $20, $10, and $5 bills is ______
if there are 5 $1 bills, the amount remaining is $45; the number of ways to make $45 using $20, $10, and $5 bills is ______
if there are 10 $1 bills, the amount remaining is $40; the number of ways to make $40 using $20, $10, and $5 bills is ______
...
if there are 40 $1 bills, the amount remaining is $10; the number of ways to make $10 using $20, $10, and $5 bills is ______
if there are 45 $1 bills, the amount remaining is $5; the number of ways to make $5 using $20, $10, and $5 bills is ______
if there are 50 $1 bills, the amount remaining is $0; the number of ways to make $0 using $20, $10, and $5 bills is ______&lt;br&gt;&lt;/pre&gt;
So you have 11 cases to work separately.  However, if you are careful and organized with your work, you can see a pattern that helps you complete the problem without working out all 11 cases completely.&lt;br&gt;
Here are the workings for a couple of the cases.&lt;br&gt;
Case 1:  Suppose there are 10 $1 bills; that leaves $40 to be made with $20, $10, and $5 bills.&lt;br&gt;
If there are 2 $20 bills, that is the whole remaining $40; there is only 1 way to complete this case using 2 $20 bills.
If there is 1 $20 bill, that leaves $20.  There are 3 choices for the number of $10 bills to use to make that remaining $20 -- 0, 1, or 2.  Whatever isn&#39;t made up with the $10 bills will be made with the $5 bills.  So there are 3 ways to complete this case using 1 $20 bill.
If there are no $20 bills, that leaves $40; that gives 5 choices for the number of $10 bills to use -- 0, 1, 2, 3, or 4; and again the $5 bills will make up whatever the $10 bills don&#39;t.  So there are 5 ways to complete this case using no $20 bills.&lt;br&gt;
So for the case where there are 10 $1 bills, the number of ways to make change for $50 is 1+3+5 = 9.&lt;br&gt;
Case 2: Suppose there are 35 $1 bills, leaving $15 to be made using the $20, $10, and $5 bills.&lt;br&gt;
Obviously we can&#39;t have any $20 bills; so we need to make the remaining $15 with only $10 and $5 bills.  As before, we have 2 choices for the number of $10 bills to use -- 0 or 1 -- and the $5 bills will make up what is left.&lt;br&gt;
So for the case where there are 35 $1 bills, there are only 2 ways to make change for the $50 bill.&lt;br&gt;
Do the similar analyses for the other cases to find the answer.

</PRE>