Question 364075
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In making a sum of money, he has 2 choices for each coin: include it, or not.  With 5 coins, the number of combinations of choices he can make -- and therefore the number of different sums of money he can make -- is 2*2*2*2*2 = 2^5 = 32.<br>
One of those possibilities is 0 (if he chooses not to include every coin in his selection).  Since you say the answer to the question is 31, apparently a sum of 0 is not allowed.<br>
Since all the other sums are allowed, the number of (nonzero) sums he can make is 32-1 = 31.