There are 5C3+5C4+5C5 ways to choose the coins.
Now, are there any sums which can be made in more than one way? If so, then they'd be counted twice.
How many different sums of money are possible using at least 3 coins from a collection consisting of one penny, one nickel, one dime, on quarter and one loonie?
2 answers
The most cases come from 3 coins at a time, 5C3 as Steve stated, there are 10 of those.
Let's consider any duplication of sums in those.
PND -- 16 cents
PNQ -- 31
PNL -- 106
PDQ -- 36
PDL -- 111
PQL -- 126
NDQ -- 40
NDL -- 115
NQL -- 130
DQL -- 135
Four at a time:
PNDQ - 41
PNDL -- 116
PNQL -- 131
PDQL -- 136
NDQL -- 140
And lastly, take all 5
PNDQL --- 141
Fortunately, there are no duplication of sums, so the total number of choices is 16
check my addition in the sums.
Let's consider any duplication of sums in those.
PND -- 16 cents
PNQ -- 31
PNL -- 106
PDQ -- 36
PDL -- 111
PQL -- 126
NDQ -- 40
NDL -- 115
NQL -- 130
DQL -- 135
Four at a time:
PNDQ - 41
PNDL -- 116
PNQL -- 131
PDQL -- 136
NDQL -- 140
And lastly, take all 5
PNDQL --- 141
Fortunately, there are no duplication of sums, so the total number of choices is 16
check my addition in the sums.
2 answers