.
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".