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# Alina and Adam are making boxes of truffles to give out as wedding fav

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Re: Alina and Adam are making boxes of truffles to give out as wedding fav [#permalink]
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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 $$C^2_5=10$$.

Hope it's clear.
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Re: Alina and Adam are making boxes of truffles to give out as wedding fav [#permalink]
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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: Alina and Adam are making boxes of truffles to give out as wedding fav [#permalink]
VeritasPrepKarishma niks18 pushpitkc pikolo2510 chetan2u

What is incorrect in below approach:
Category 1 of truffle can be selected in 5C1 (out of 5 different varieties, I need to choose 1)
Category 2 of truffle can be selected in 4C1 (out of 4 available varieties, I need to choose 1)

Hence: Final ans: 5C1 * 4C1
AND means to multiply since I want two different types of truffle in box
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Re: Alina and Adam are making boxes of truffles to give out as wedding fav [#permalink]
2
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VeritasPrepKarishma niks18 pushpitkc pikolo2510 chetan2u

What is incorrect in below approach:
Category 1 of truffle can be selected in 5C1 (out of 5 different varieties, I need to choose 1)
Category 2 of truffle can be selected in 4C1 (out of 4 available varieties, I need to choose 1)

Hence: Final ans: 5C1 * 4C1
AND means to multiply since I want two different types of truffle in box

Hi...

By doing 5C1*4C1, you are choosing two -- one after another
Say five different types are A,B,C,D,E
But here the order does not matter AB in the box is same as BA in the box
So either divide your result by 2 so 5*4/2=10
Or choose 2 out of 5 = 5C2=5!/(3!2!)=10
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Re: Alina and Adam are making boxes of truffles to give out as wedding fav [#permalink]
VeritasPrepKarishma niks18 pushpitkc pikolo2510 chetan2u

What is incorrect in below approach:
Category 1 of truffle can be selected in 5C1 (out of 5 different varieties, I need to choose 1)
Category 2 of truffle can be selected in 4C1 (out of 4 available varieties, I need to choose 1)

Hence: Final ans: 5C1 * 4C1
AND means to multiply since I want two different types of truffle in box

Lets say the five truffles are A,B,C,D, and E

Category one - A | Category two - C
is the same as
Category one - C | Category two - A

So, the final possibilities for the truffles in the box are $$\frac{C_1^5 * C_1^4}{2} = 5*\frac{4}{2} = 10$$

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Re: Alina and Adam are making boxes of truffles to give out as wedding fav [#permalink]
VeritasPrepKarishma niks18 pushpitkc pikolo2510 chetan2u

What is incorrect in below approach:
Category 1 of truffle can be selected in 5C1 (out of 5 different varieties, I need to choose 1)
Category 2 of truffle can be selected in 4C1 (out of 4 available varieties, I need to choose 1)

Hence: Final ans: 5C1 * 4C1
AND means to multiply since I want two different types of truffle in box

By using this method, AB and BA are two different combinations. But according to the question, position doesn't matter. Hence you need to divide by 2 to remove the duplicates

The other way to solve this , just use combination formula 5C2. Answer is 10
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Re: Alina and Adam are making boxes of truffles to give out as wedding fav [#permalink]
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 have the same issue, if someone could answer ?
Re: Alina and Adam are making boxes of truffles to give out as wedding fav [#permalink]
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