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word problem please help
- Thread starter arzfan
- Start date
HallsofIvy
Elite Member
- Joined
- Jan 27, 2012
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- 7,763
A good strategy for problems like this is to start by doing a simpler version. Suppose there was one heart that could be colored "red, pink, or blue". How many ways could it be colored? That should be easy! Three, of course, R, P, or B (writing "R" for "red", "P" for "pink", and "B" for "blue", of course).
Suppose there were two hearts. That's only a little harder- you might write out each possible combination:
RR
RP
RB
PR
PP
PB
BR
BP
BB.
Notice that I have taken the "R", "P", "B" for one and appended the same three letters for the second.
How many is that? You could make the same kind of chart for three hearts, taking each of those with "R", "P", or "B" added to the end- but you should be able to see a numerical pattern.
Do you know the "fundamental counting principle"?
Suppose there were two hearts. That's only a little harder- you might write out each possible combination:
RR
RP
RB
PR
PP
PB
BR
BP
BB.
Notice that I have taken the "R", "P", "B" for one and appended the same three letters for the second.
How many is that? You could make the same kind of chart for three hearts, taking each of those with "R", "P", or "B" added to the end- but you should be able to see a numerical pattern.
Do you know the "fundamental counting principle"?
YES.so would the answer be 21?
[We have assumed the three hearts are identified, so that you always know which is which even when the colors move around. If that is not true, then we only know how many have a given color, but not which ones. Then when you count, RPB would look the same as RBP or PRB, and so forth. Then the number of different combinations would be much smaller.]
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