Question 364075
Selecting 1 coin out of  5 coins: 5C1=5  different sums
Selecting 2 coins out of 4 coins: 5C2=10 different sums
Selecting 3 coins out of 4 coins: 5C2=10 different sums
Selection 4 coins out of 4 coins: 5C4=5  different sums
Selection 5 coins out of 4 coins  5C5=1  different sums
Hence total number of different sums of money :5+10+10+5+1= 31 Answer