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# For a fundraising dinner, a florist is asked to create flowe

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Senior Manager
Joined: 21 Oct 2013
Posts: 414
For a fundraising dinner, a florist is asked to create flowe  [#permalink]

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11 Apr 2014, 15:40
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Difficulty:

45% (medium)

Question Stats:

67% (01:50) correct 33% (01:50) wrong based on 184 sessions

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For a fundraising dinner, a florist is asked to create flower arrangements for 8 tables. Each table can have one of the two types of bouquets available, one with a single type of flower or one with three different types of flowers. If the florist wants to make each table unique, what is the least number of types of flowers he needs?
A) 4
B) 5
C) 6
D) 7
E) 8

OE:
Looking for (n + nC3) = 8
2 types of flower arrangements: some with 1 flower and some with 3 different flowers.
Therefore, total number of arrangements we could make from n different types of flowers = (n + nC3).
Since 4C3 = 4 (nC(n-1) always equals n combinations i.e. nC(n-1) = n), (n + nC3) = (4 + 4C3) = (4 + 4) = 8
Aim to get 8 distinct floral arrangements, 4 different types of flowers is the answer.

Hi, I want to know whether this reverse combination calculation is actually the GMAT style question, please.
Personally, I have never come across with this type of calculation.
Math Expert
Joined: 02 Sep 2009
Posts: 56267
Re: For a fundraising dinner, a florist is asked to create flowe  [#permalink]

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12 Apr 2014, 03:45
1
1
goodyear2013 wrote:
For a fundraising dinner, a florist is asked to create flower arrangements for 8 tables. Each table can have one of the two types of bouquets available, one with a single type of flower or one with three different types of flowers. If the florist wants to make each table unique, what is the least number of types of flowers he needs?
A) 4
B) 5
C) 6
D) 7
E) 8

OE:
Looking for (n + nC3) = 8
2 types of flower arrangements: some with 1 flower and some with 3 different flowers.
Therefore, total number of arrangements we could make from n different types of flowers = (n + nC3).
Since 4C3 = 4 (nC(n-1) always equals n combinations i.e. nC(n-1) = n), (n + nC3) = (4 + 4C3) = (4 + 4) = 8
Aim to get 8 distinct floral arrangements, 4 different types of flowers is the answer.

Hi, I want to know whether this reverse combination calculation is actually the GMAT style question, please.
Personally, I have never come across with this type of calculation.

Yes, it is a GMAT style question. Below are bunch of similar questions to practice:

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Hope this helps.
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Posts: 225
Location: India
Re: For a fundraising dinner, a florist is asked to create flowe  [#permalink]

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12 Apr 2014, 21:01
I don't understand the explanation.How do we arrive at the equation:$$n+C(n,3)=8$$?

If we take 8 different types of single flower bouquet then only we can have each table unique.

On the other hand,if we take 4 different types of flowers and decorate 4 tables with single flowers and the other four with different combinations of the 4 types of flowers won't the latter 4 tables essentially be familiar as the type of flowers remain the same irrespective of how we arrange them?

Bunuel,could you take on this one please?
Intern
Joined: 10 Apr 2014
Posts: 32
Re: For a fundraising dinner, a florist is asked to create flowe  [#permalink]

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13 Apr 2014, 04:41
1
AKG1593 wrote:
I don't understand the explanation.How do we arrive at the equation:$$n+C(n,3)=8$$?

If we take 8 different types of single flower bouquet then only we can have each table unique.

On the other hand,if we take 4 different types of flowers and decorate 4 tables with single flowers and the other four with different combinations of the 4 types of flowers won't the latter 4 tables essentially be familiar as the type of flowers remain the same irrespective of how we arrange them?

Bunuel,could you take on this one please?

Suppose you take n different type of flowers, so you can have n single flower bouquets.

C(n, 3) means number of unique combinations of 3 from n objects.
So, if n = 4, C (4, 3) = 4!/((4-3)!*3!) = 4

Also, we can have 4 unique combination of 3 flowers, hence all these 4 bouquets will be different from each other.
and with 4 different flowers we can make 4 different single flower bouquets

So, all together we will have 8 different type of bouquets

------------------------------------
Kudos if the answer helped
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Joined: 06 Sep 2013
Posts: 1649
Concentration: Finance
Re: For a fundraising dinner, a florist is asked to create flowe  [#permalink]

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20 May 2014, 05:10
Let me see if I got this right. So we have 8 tables and we have two types of bouquet which can be either single flowers or a combination of three different flowers

If n=4

Then we can have 4c3 = 4 combinations of three different flowers plus 4 combinations if each of those flowers are used as single flowers.

Therefore 4+4=8

Hope this clarifies
Cheers
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Posts: 2540
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: For a fundraising dinner, a florist is asked to create flowe  [#permalink]

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26 Oct 2016, 07:16
goodyear2013 wrote:
For a fundraising dinner, a florist is asked to create flower arrangements for 8 tables. Each table can have one of the two types of bouquets available, one with a single type of flower or one with three different types of flowers. If the florist wants to make each table unique, what is the least number of types of flowers he needs?
A) 4
B) 5
C) 6
D) 7
E) 8

I decided to try some "values", since we don't have to count that many options...
suppose we have 4 different types of flowers:
A
B
C
D
we already have covered 4 tables, if we put 1st option.
then, we need to select 3 of them for the 2nd option...
ABC
BCD
ACD
ABD
alternatively, 4C3, which is 4...
4+4 = 8
thus, with 4 types of flowers, we can cover all 8 tables so that no arrangement is repeated.
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Re: For a fundraising dinner, a florist is asked to create flowe  [#permalink]

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24 Feb 2018, 11:41
1
Hi All,

TESTing THE ANSWERS is a great way to tackle this type of question. You can also solve it using the Combination Formula and doing a bit of math.

Combinations = N!/K!(N-K)! Where N is the total number of items and K is the number of items in the 'subgroup'

The question asks to form 8 different flower bouquets using groups of flowers. We can make a bouquet with just 1 type of flower or 3 different types of flowers. We're asked for the LEAST number of different types of flowers needed to create 8 different bouquets.

With 4 different types of flower, we could have....

Bouquets with just 1 flower = 4c1 = 4!/(1!3!) = 4 different options

Bouquets with 3 different flowers = 4c3 = 4!/(3!1!) = 4 different options

Here, we have 4+4 = 8 different options, which is exactly what we're looking for. This MUST be the answer.

GMAT assassins aren't born, they're made,
Rich
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Re: For a fundraising dinner, a florist is asked to create flowe   [#permalink] 24 Feb 2018, 11:41
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