MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

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MATHCOUNTS TOOLBOX Facts, Formulas and Tricks
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Lesson 10 Combinations
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When different orderings are not to be counted
separately, i.e. the outcome, mn is equivalent to
the outcome nm, the problem involves combinations.
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Combination FormulaDifferent orders of the same
items are not counted.  The combination formula
is equivalent to dividing the corresponding
number of permutations by r!.n number of
available items or choicesr the number of items
to be selected    Sometimes this formula is
written C(n,r).
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Combination FormulaDifferent orders of the same
items are not counted.  The combination formula
is equivalent to dividing the corresponding
number of permutations by r!.n number of
available items or choicesr the number of items
to be selected    Sometimes this formula is
written C(n,r).
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Taking the letters a, b, and c taken two at a
time, there are six permutations ab, ac, ba,
bc, ca, cb.  If the order of the arrangement is
not important, how many of these outcomes are
equivalent, i.e. how many combinations are there?
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Taking the letters a, b, and c taken two at a
time, there are six permutations ab, ac, ba,
bc, ca, cb.  If the order of the arrangement is
not important, how many of these outcomes are
equivalent, i.e. how many combinations are there?
ab ba ac ca and bc cbThe three
duplicate permutations would not be counted,
therefore three combinations exist
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Calculate the value of 7C4.
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Calculate the value of 7C4. This represents a
combination of 7 objectstaken 4 at a time and is
equal to
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Calculate the value of 7C4. This represents a
combination of 7 objectstaken 4 at a time and is
equal to
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Calculate the value of 9C5
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Calculate the value of 9C5 This represents a
combination of 9 objects taken 5 at a time and is
equal to . . .
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Calculate the value of 9C5 This represents a
combination of 9 objects taken 5 at a time and is
equal to . . .
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In how many ways can three class representatives
be chosen from a group of twelve students?  If
the order of the arrangement is not important,
how many outcomes will there be? 
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In how many ways can three class representatives
be chosen from a group of twelve students?  If
the order of the arrangement is not important,
how many outcomes will there be?  This
represents a combination of 12 objects taken 3 at
a time and is equal to
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In how many ways can three class representatives
be chosen from a group of twelve students?  If
the order of the arrangement is not important,
how many outcomes will there be?  This
represents a combination of 12 objects taken 3 at
a time and is equal to
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Fini!