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Hints and solutions to
Make a List #7
How many different four-digit numbers can be formed using the digits
1, 1, 9, and 9?
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We're back to making systematic lists.
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This one isn't too hard to just list all the possibilities:
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We'll try and list them in numerical order to make sure we don't
miss any.
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There's 1199, 1919, 1991, 9119, 9191, and finally 9911.
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So there are
six different four-digit numbers that can be made
this
way.
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An "abstract" way to figure this out (without writing all the
numbers down) is
to consider that to choose one of the numbers, it's enough to pick the
two places where
the 1's go, then the other two places have to have 9's. (Or vice versa:
pick the two
places where the 9's go). So the number of such numbers is equal to the
number of
ways to choose two things from four, or C(4,2) = 4 x 3 / (2 x 1) =
6.
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