<p>I’m terrible at probability; I saw this question n the Barron’s prep book and was totally stumped. The explanation was beyond me.</p>
<p>A purse contains five different coins (penny, nickel, dime, quarter, half-dollar). How many different sums of money can be made using one or more coins?
A: 5
B: 10
C: 32
D: 120
E: None of the above</p>
<p>(Answer=E)</p>
<p>A purse contains five different coins (penny, nickel, dime, quarter, half-dollar). How many different sums of money can be made using one or more coins?
A: 5
B: 10
C: 32
D: 120
E: None of the above</p>
<p>Ok just add “cents” to everything I write …</p>
<p>penny=1, nickel=5, dime=10, quarter=25, half-dollar=50</p>
<p>Using 1 coin: 5 ways (make sense? How many ways can you grab 1 coin out of a purse when there are 5? 5 right … mathmatically it is 5 nCr 1, if that makes it easier) … you can grab any coin and get a different value since all of the coins have different cent values
Using 2 coins: this is a little more tricky it’s 5 nCr 2. That’s 10 when you plug it into your calc. Now ask yourself, do any repeat? Meaning, can any two coins you grab have a value that we counted in the “using 1 coin” problem? Rememer we only have 1 of each of the coins (I think, it’s sort of ambiguous)
Using 3 coins: 5 nCr 3 = 10
Using 4 coins: 5 nCr 4 = 5
Using 5 coins: 5 nCr 5 = 1
5+10+10+5+1=31. The answer looks like 31, assuming none of these values repeat … meaning each combination counted above has a unique value … ex. a penny, nickel, and dime total 16 cents. Would any other combo make 16 cents? Try … you won’t be able to any other way.
So, the answer looks like 31, maybe a little less if some repeat but I see none, so E looks good! Does that help?</p>
<p>Thanks a lot, yeah I undestand the problem a lot better.
I’m beginning to grasp individual probability questions now, but I still can’t get a coherent understanding of the entire unit.
The Barron’s book is ridiculously dense and concise; do you know of any other books that might give a better explanation?
Again, thanks :).</p>
<p>the answer is E</p>