Question 943931: Tom has a $20 bill, a $10 bill, a $5 bill, and $1 bill. List the total costs possible for items he could buy if he receives no change.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The cost, in $, of an item that could be purchased receiving no change is
 where
 ,  ,  , and  are  or  .
That means 2 choices for each variable, and
 choices overall.
One of those  choices is .
I suppose $0 would mean not buying anything,
so if some amount was paid,
it has to be one of the remaining  possible amounts.
Now that I know there are 15, I list the amounts,
and count them to make sure I do not forget any:
With a $1 bill ( ):
$1,
and if we also add a $5 bill ( ),
$1+$5=$6
$1+$5+$10=$16
$1+$5+$10+$20=$36
$1+$5+$20=$26
With a $1 bill, and a $10 bill, but no $5 bill ( ),
$1+$10=$11
$1+$10+$20=$31
With a $1 bill, and another bill, but no $5 or $10 bill,
$1+$20=$21
With no $1 bill  ), but including one $5 bill (  ):
$5
$5+$10=$15
$5+$10+$20=$35
$5+$20=$25
If no $1 or $5 bill is used (  ):
$10
$10+$20=$30
$20
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