61 - 44 = 17,  


therefore, if I correctly understand the question, it is the same as to ask


    by how many ways 17 cents can be presented as a combination of 5, 3 and 2 cents.


I see these combinations


1)  17 =  5 + 5 + 5 + 2


2)  17 = 5 + 5 + (3+2) + 2


3)  17 = 5 + (3+2) + (3+2) + 2


4)  17 = (3+2) + (3+2) + (3+2) + 2


5)  17 = 3 + 3 + 3 + 3 + 3 + 2


6)  17 = 3 + 2 + 2 + 2 + 2 + 2 + 2 + 2


7)  17 = 5 + 2 + 2 + 2 + 2 + 2 + 2


and do not see any other combinations.


My answer is "7 combinations".