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College Algebra - Floral Combinations











































Combinations and Permutations

Jeannie Baker makes floral arrangements.

She has 16 different cut flowers, and plans to use 6 of them.

How many different selections of the 6 flowers are possible?

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Jun 13, 2013
Combinations
by: Staff


Answer

Part I


Does the order in which the 6 flowers are used make a difference?

Is the arrangement of the six flowers {1, 2, 3, 4, 5, 6} the same as the arrangement of the same six flowers in a different order {6, 5, 4, 3, 2, 1}?


If the order (the sequential arrangement of the flowers used in the floral display) does not matter, it is called a Combination.

A Combination means that the arrangement of the same six flowers can be in any order.

{1, 2, 3, 4, 5, 6} is the same as the arrangement of the same six flowers in this order {6, 5, 4, 3, 2, 1} or this order {4, 5, 6, 3, 2, 1}, and so on.

These three display arrangements are counted a one combination. All three floral arrangements use exactly the same flowers, regardless of the order.


If the order (the sequential arrangement of the flowers used in the floral display) is important, it is called a Permutation.

The permutation is a list of all possible floral arrangements.

A Permutation means that the arrangement of the six flowers {1, 2, 3, 4, 5, 6} is the NOT same as the arrangement of the same six flowers {6, 5, 4, 3, 2, 1} is the NOT same as {4, 5, 6, 3, 2, 1}, and so on.

These three floral arrangements are counted a three permutations. All three floral arrangements may use the same flowers, but the order is different.

Combinations

The problem statement asks "How many different selections of the 6 flowers are possible?"

Nothing is said about how to arrange the six flowers after they are selected.

Because of this, I'm assuming the order in which the flowers are displayed does not matter.

That means the question is asking for the number of combinations (rather than the number of permutations).

The formula for computing the number of all possible combinations is:


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Jun 13, 2013
Combinations
by: Staff


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Part II

Formula for computing the number of possible combinations





0 ≤ r ≤ n.
n = the number different cut flowers ( = 16)
r = number of flowers chosen (= 6)

Order is not important

Repetition is not allowed


Compute possible combinations of selecting 6 flowers from a group of 16 different flowers






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Jun 13, 2013
Combinations
by: Staff


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Part III


The final answer - the number of possible ways to select the 6 flowers:


Number of possible ways to select a combination of 6 flowers from a group of 16 different flowers







Thanks for writing.

Staff
www.solving-math-problems.com


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