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

Question

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.

Bunuel · Accepted Answer

Yes, it is a GMAT style question. Below are bunch of similar questions to practice: each-student-at-a-certain-university-is-given-a-four-charact-151945.html all-of-the-stocks-on-the-over-the-counter-market-are-126630.html if-a-code-word-is-defined-to-be-a-sequence-of-different-126652.html a-4-letter-code-word-consists-of-letters-a-b-and-c-if-the-59065.html a-5-digit-code-consists-of-one-number-digit-chosen-from-132263.html a-company-that-ships-boxes-to-a-total-of-12-distribution-95946.html a-company-plans-to-assign-identification-numbers-to-its-empl-69248.html the-security-gate-at-a-storage-facility-requires-a-five-109932.html all-of-the-bonds-on-a-certain-exchange-are-designated-by-a-150820.html a-local-bank-that-has-15-branches-uses-a-two-digit-code-to-98109.html a-researcher-plans-to-identify-each-participant-in-a-certain-134584.html baker-s-dozen-128782-20.html#p1057502 in-a-certain-appliance-store-each-model-of-television-is-136646.html m04q29-color-coding-70074.html john-has-12-clients-and-he-wants-to-use-color-coding-to-iden-107307.html how-many-4-digit-even-numbers-do-not-use-any-digit-more-than-101874.html a-certain-stock-exchange-designates-each-stock-with-a-85831.html the-simplastic-language-has-only-2-unique-values-and-105845.html m04q29-color-coding-70074.html a-researcher-plans-to-identify-each-participant-in-a-certain-134584-20.html Hope this helps.

AKG1593 · Answer

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?

ind23 · Answer

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

jlgdr · Answer

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

Answer: A

Hope this clarifies
Cheers

mvictor · Answer

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.

EMPOWERgmatRichC · Answer

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.

Let's start with the SMALLEST Answer.

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.

Final Answer:  A

GMAT assassins aren't born, they're made, 
Rich

Paras96 · Answer

For 8 tables,

With the help of 3 different flowers, we can make 3! = 6 unique arrangements
Also with 2 of 3 different flowers used above, we can utilise them for = 2 unique arrangements

Therefore, we can use 3 different flowers as the least.

Please clarify

Ishmeet7 · Answer

No you can't. Let's say your 3 flowers are A,B,C. 
If you arrange them as ABC; that is the same as BCA. i.e. ABC=CBA. Order does not matter so it won't be counted as a separate case.

So your tables will be A, B, C, ABC. The other 4 tables won't have any flowers.

More than depending on combinatorics, solve this sum intuitively.

_ _ _ _ _ _ _ _

8 tables ^

And say 4 flowers - ABCD.

A B C D  (4 tables) and  ABC BCD CDA ABD 
  other 4 tables.

Draw it out and you'll be able to solve it!

Hope this helps!

egmat · Answer

Hi Paras96,

Great question! The  key insight  is that a bouquet is a *selection* of flowers, not an ordered arrangement. A bouquet containing Rose, Tulip, and Lily is the SAME bouquet regardless of order — you can't distinguish it from one with Lily, Rose, and Tulip. So order does NOT matter here.

This means we use  Combinations , not  Permutations .

With  3  types of flowers:
- Single-flower bouquets:  3  (one per flower type)
- Three-flower bouquets: C( 3 , 3 ) =  1  (there's only ONE way to pick  3  flowers from  3  — you must pick all of them)
- Total unique arrangements =  3  +  1  =  4  — NOT enough for  8  tables.

Your mistake was calculating  3!  =  6 , which counts different orderings of the same  3  flowers as different bouquets.  But {Rose, Tulip, Lily} arranged in any order on a table is still the same bouquet.

Now with  4  types of flowers: 
- Single-flower bouquets:  4 
- Three-flower bouquets: C( 4 , 3 ) =  4  (pick any  3  out of  4 )
- Total =  4  +  4  =  8  — exactly what we need!

So the answer is  4 .

Answer: A

General principle:  Whenever a problem asks about *groups* or *selections* (like bouquets, committees, teams), order doesn't matter — use  Combinations .  Permutations  only apply when the arrangement or sequence matters (like seating order or rankings).

AdityaHarsh · Answer

No, suppose you take 4 different types of flowers namely a,b,c,d for the first 4 tables respectively. (i.e. a on first, b on second, c on third, d on fourth).
Then the combinations for the latter 4 tables will be like:
For table 5: Suppose a combination of a,b,c
For table 6: a combination of b,c,d
For table 7: a combination of c,d,a
For table 8: a combination of a,c,d
Note that at least one flower type is different in each combination which makes it unique.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards