combinatorics confusion

Rahul@gurome wrote:

Gurpinder 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?


5!/3!=20. which is wrong.

5!/2!3!=10 is right. why should the 2! be there.

The word thats confusing me is "If each box holds 2 truffles of different types".

2 truffles of different types means out of 5 different types of truffles, there will be 2 different truffles in each box.
So, the no. of different boxes that can be made = 5!/(2!3!) = 10

Does that help?

Hey Rahul,

Whats confusing me there is that DIFFERENT TRUFFLES word. Doesent that mean that the order is important since the truffles are distinguishable. and since they are distinguishable, that means its a permutation proble,.

??

Gurpinder wrote:

Rahul@gurome wrote:

Gurpinder 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?


5!/3!=20. which is wrong.

5!/2!3!=10 is right. why should the 2! be there.

The word thats confusing me is "If each box holds 2 truffles of different types".

2 truffles of different types means out of 5 different types of truffles, there will be 2 different truffles in each box.
So, the no. of different boxes that can be made = 5!/(2!3!) = 10

Does that help?

Hey Rahul,

Whats confusing me there is that DIFFERENT TRUFFLES word. Doesent that mean that the order is important since the truffles are distinguishable. and since they are distinguishable, that means its a permutation proble,.

??

Remember the question here is asking about different boxes. How the boxes are packaged inside would not matter, Think about it this way. Imagine that you have Truffles of Type A, B, C, D and E. A box consisting of Type A and Type B is no different than a box that consists of Type B and Type A. That is why their are 10 different boxes of Truffles

Hi. I am still a bit confused with the wording of these questions. Could you further elaborate why we can't treat this as a distinguishable question type?

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"

Before you start solving any kind of counting problems, decide whether order matters. In this case, question actually asks how many ways can you put two different truffles out of 5 truffles in a single box (even though the order of words has been changed in the rephrased question, underlying meaning is the same.) Because the order doesn't matter, use combination!