Question 364075
As there are 5 coins, for every sum any particular coin may be selected or not.

thus, for each sum, there are two possibilities of each coin.

for example, let A,B,C,D AND E are coins, then sum can be get

ABCDE
1 1 1 1 1
1 1 1 1 0
 :
 : 
 :
0 0 0 0 1
0 0 0 0 0  ( no one coin selected)

Here 1 represent it is included and 0 represent not included.



total no. of different sum = 2^5 - 1 = 31

 
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