Mgmat combos question

Question

Ok here is a problem from mgmat that I don't agree with the answer. Please advise

Amy and Adam are making boxes of truffles for 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.

The book says it's 5!/3!2! but this seems wrong since there is a unlimited supply. Instead I would think u have 5 choices for the first and 4 for the second hense 20

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LJ · Answer

There's an unlimited supply, but that is irrelevant since the question specifies that each box must hold two different types of truffles. Therefore it is 5c2.

Picking 20 as an answer assumes order matters but it doesn't because {A,B} is the same box of truffles as {B,A}.

vitamingmat · Answer

Well. Hope below ans help you.
 They have an unlimited supply of 5 different types of truffles. So, total truffles available are = 5 types only..
Out of 5, you can fix 2 turffles in a box ===> from 5 u need to select 2 ===> 5c2 = 5!/(5-2)!2!

===> 5!/3!2!

like the ans, Kudos me

ezhilkumarank · Answer

It is a test of combination concept since a box with 2 truffles AB or BA are considered to be the same and hence you need to divide the result of (First choice of truffle * second choice) of truffles --> 5*4  by 2 .

This leads to the answer given in the book --- 5!/((2!)*(3!)) -- 10.

jpr200012 · Answer

To use MGMAT's anagram method, let Y = included and N = not included. This would give YYNNN. So it would be 5!/(3!2!).

metallicafan · Answer

The questions asks "how many   different   boxes can they make". The unlimited supply is irrelevant.

Therefore 5!/(2!*3!) = 10

cabelk · Answer

Bag of 5 choices.

Combo box arrangement
(_)(_)/2!

First position has 5 choices. Second position has 4 choices.
(5)(4)/2!

5!/3!2! = (5)(4)(3)(2)(1)/(3)(2)(1)(2)(1) = (5)(4)/2!

Mgmat combos question

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