Question 44520: Make an orderly list of all possible outcomes resulting from tossing a penny, a nickel, and a dime.
Found 2 solutions by checkley71, AnlytcPhil:
Answer by checkley71(8403)   (Show Source):
Answer by AnlytcPhil(1806)  (Show Source):
You can put this solution on YOUR website! Make an orderly list of all possible outcomes resulting from tossing
a penny, a nickel, and a dime.
1. Start out with H for each
2. To get the next case start from the right and go left.
Change the first H you come to
3. If there are any to the right of the one you changed to T,
CHANGE THEM ALL TO h
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Start out with H for each
Penny Nickel Dime
H H H
To get the next case start from the right and go left.
Change the first H we come to to T.
The first H we come to going right to left on
H H H
is the H under "Dime". So we change that H to T. So we have
H H T
There are none to the right of the one we changed, so we
write that underneath and so far we have:
Penny Nickel Dime
H H H
H H T
To get the next case we again start from the right and go
left on the bottom line.
Change the first H you come to T.
The first H we come to going right to left on
H H T
is the H under "Nickel". So we change that H to T. So we have
H T
There is one T to the right of the one we just changed, so we
change that to H, getting
H T H
and write that underneath, and so far we we have:
Penny Nickel Dime
H H H
H H T
H T H
To get the next case, start from the right and go left on the
bottom line.
Change the first H you come to to T.
The first H we come to going right to left on
H T H
is the H under "Dime". So we change that H to T. So we have
H T T
There are none to the right of the one we changed, so we
write that underneath and so far we have:
Penny Nickel Dime
H H H
H H T
H T H
H T T
To get the next case we again start from the right and go
left.
Change the first H you come to T.
The first H we come to going right to left on
H T T
is the H under "Penny". So we change that H to T. So we have
T
There are two T's to the right of the one we just changed, so we
change both to H, getting
T H H
and write that underneath, and so far we we have:
Penny Nickel Dime
H H H
H H T
H T H
H T H
T H H
To get the next case, start from the right and go left.
Change the first H you come to to T.
The first H we come to going right to left on
T H H
is the H under "Dime". So we change that H to T. So we have
T H T
There are none to the right of the one we changed, so we
write that underneath and so far we have:
Penny Nickel Dime
H H H
H H T
H T H
H T H
T H H
T H T
To get the next case we again start from the right and go
left.
Change the first H you come to T.
The first H we come to going right to left on
T H T
is the H under "Nickel". So we change that H to T. So we have
T T
There is one T to the right of the one we just changed, so we
change that to H, getting
T T H
and write that underneath, and so far we we have:
Penny Nickel Dime
H H H
H H T
H T H
H T T
T H H
T H T
T T H
To get the next (final) case start from the right and go left.
Change the first H you come to to T.
The first H we come to going right to left on
T T H
is the H under "Dime". So we change that H to T. So we have
T T T
T T H
and write that underneath, and so far we we have:
Penny Nickel Dime
H H H
H H T
H T H
H T T
T H H
T H T
T T H
T T T
There are no H's left in the bottom line, so we
are done.
Edwin
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