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Amy and Adam are making boxes of truffles to give out as wed [#permalink]
20 Jun 2011, 19:16

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Difficulty:

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Question Stats:

80% (01:41) correct
20% (00:43) wrong based on 1 sessions

Amy and Adam are making boxes of truffles to give out as wedding favors. They have an unlimited supply of 5 different types of truffles. If each box holds 2 truffles of different types, how many different boxes can they make?

I understand these are all the possible combinations:

Box 1: A B Box 2: A C Box 3: A D Box 4: A E Box 5: B C Box 6: B D Box 7: B E Box 8: C D Box 9: C E Box 10: D E

But I don't get the mathematical interpretation of this.. 5! / (3! * 2!)

Re: MGMAT Word Translations COMBINATORICS!!! [#permalink]
21 Jun 2011, 01:39

Expert's post

Mahtab wrote:

Amy and Adam are making boxes of truffles to give out as wedding favors. They have an unlimited supply of 5 different types of truffles. If each box holds 2 truffles of different types, how many different boxes can they make?

I understand these are all the possible combinations:

Box 1: A B Box 2: A C Box 3: A D Box 4: A E Box 5: B C Box 6: B D Box 7: B E Box 8: C D Box 9: C E Box 10: D E

But I don't get the mathematical interpretation of this.. 5! / (3! * 2!)

I don't get how the anagram can be "YYNNN"

You can think of it in 2 ways: 1. You have 5 different types of truffles. For each box, you have to select 2 different types of truffles. In how many ways can you do it? 5C2 = 5!/3!*2! (When out of n things, you have to select r, you can do it in nCr ways. nCr = n!/r!*(n-r)! For more on this, check out Combinatorics & Probability by Veritas Prep) 2. There are 5 truffles. You need to select 2 and not select the rest of the three. Y - select a truffle. N - Do not select it So you can select 2 truffles in the number of ways in which you can arrange YYNNN. YYNNN means you select the first 2 and leave the rest. YNYNN means you select 1st and 3rd and leave the rest. etc... This can be done in 5!/2!*3! You can arrange 5 things in 5! ways. But you have 2 Ys and 3 Ns so you divide by 2! and 3!. (Again, for more on this, check out Combinatorics & Probability by Veritas Prep)

Re: MGMAT Word Translations COMBINATORICS!!! [#permalink]
21 Jun 2011, 04:37

Yeah I was doing so well in Quant up until I hit Guide 4 of MGMAT Combinatorics...they did an adaquete job at explaining it so I bought the Veritas Combinatorics book from amazon last night! I will put this to rest for a few days I guess and move on to statistics.

Thanks and I kind of understand the nCr thing but I want to go more in depth of the concept so I have a strong foundation.

Re: Amy and Adam are making boxes of truffles to give out as wed [#permalink]
20 Jul 2013, 10:49

Hi, I have an issue with comprehending such problems. Could any of you correct me please. I know the solution to the problem is 10.

My approach is : Each box can contain two truffles, so if I say there are two slots in the box then the first slot has the possibility of 5 different types of truffles and the next slot has the possibility of 4 different types of truffles. So i concluded 5*4 = 20 as the answer.

Can any of you please identify the flaw in my approach to the problem. Again, I know the solution, but I want to know what exactly is the flaw in the argument presented above, so that I don't repeat the mistake again.

Re: Amy and Adam are making boxes of truffles to give out as wed [#permalink]
20 Jul 2013, 11:14

1

This post received KUDOS

Expert's post

kiranck007 wrote:

Hi, I have an issue with comprehending such problems. Could any of you correct me please. I know the solution to the problem is 10.

My approach is : Each box can contain two truffles, so if I say there are two slots in the box then the first slot has the possibility of 5 different types of truffles and the next slot has the possibility of 4 different types of truffles. So i concluded 5*4 = 20 as the answer.

Can any of you please identify the flaw in my approach to the problem. Again, I know the solution, but I want to know what exactly is the flaw in the argument presented above, so that I don't repeat the mistake again.

The problem with your solution is that 20 has duplications in it: box holding {A, B} is the same as the box holding {B, A} and 5*4 will give you both boxes.

The question basically asks: in how many ways we can select 2 different truffles out of 5, which is simply C^2_5=10.

Re: Amy and Adam are making boxes of truffles to give out as wed [#permalink]
20 Jul 2013, 11:17

1

This post received KUDOS

kiranck007 wrote:

Hi, I have an issue with comprehending such problems. Could any of you correct me please. I know the solution to the problem is 10.

My approach is : Each box can contain two truffles, so if I say there are two slots in the box then the first slot has the possibility of 5 different types of truffles and the next slot has the possibility of 4 different types of truffles. So i concluded 5*4 = 20 as the answer.

Can any of you please identify the flaw in my approach to the problem. Again, I know the solution, but I want to know what exactly is the flaw in the argument presented above, so that I don't repeat the mistake again.

I think you are using the slot-method. I am not very familiar with it, but you are missing the last step:

_ _ , two slots that can be filled in 5*4=20 ways. Correct till here, but then you have to divide for the "factorial" number of interchangeable slots, in this case 2!=2. So the final result is \frac{5*4}{2}=10.

_________________

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Re: Amy and Adam are making boxes of truffles to give out as wed [#permalink]
09 Jul 2014, 14:21

Can someone explain the differences in the approaches you would take if you could pick 2 of the same type of truffle vs how in this problem you can only use one type of each truffle per box?

I understand with the anagram method the latter is YYNNN - out of five choices, two of those five will be picked and three of those 5 will not be picked, therefore the answer is 5!/2!3!

But what about if dupes were allowed, how would the calculation change? Obviously that's a pretty easy thing to manually add but I'd like to understand the process.

gmatclubot

Re: Amy and Adam are making boxes of truffles to give out as wed
[#permalink]
09 Jul 2014, 14:21