maximum number of substances that can be identified using 7

as order does not matter
Y Y Y N N N N
ie
7!/(3!4!) =35

sachin_yadav wrote:Hi All,

Can you please clarify whether the following question is a permutation or a combination. I solved the question with a combination formula. I thought the word "unordered" in question means combination, but i am not sure.


The following question is:-

At a certain laboratory, chemical substances are identified by an unordered combination of 3 colors. If no chemical may be assigned the same 3 colors, what is the maximum number of substances that can be identified using 7 colors ?

(A) 21
(B) 35
(C) 105
(D) 135
(E) 210


Answer is B


Combination formula:-

nCr = n! / r! * (n - r)!

You are right, that it needs a combination formula.
Chemical substances are identified by an unordered combination of 3 colors : [Think that you are storing a particular chemical in a bottle. To remember what that substance it you have come up with an idea of coloring it with 3 colors (say, Blue, Green, Yellow). Now if the order would have mattered then, the different cases like when Yellow is written above Blue would have been different from Blue written above yellow. So, in that case we would have been dealing with arrangements of color, So that would have been a good use case for "Permutation".

In the given condition, the order where we write the colors (above/below) doesn't matter as long as they are same, so we are just worried about selecting the 3 colors (not arranging those 3 selected colors), therefore the current case is a proper use case for "Combinations". ]

Hope that helps !

Anurag@Gurome wrote:
Yes you're correct.
The word unordered means combination. And the combination formula you've given that is also correct and gives the answer 35. May be you've some confusion about what "unordered" means (in that case let me know, I'll explain) or you've made some silly mistake!

Maximum number of substances that can be identified = Number of ways to select 3 colors out of 7 = 7C3 = 7!/(3!*4!) = 35

The correct answer is B.

anshumishra wrote:
You are right, that it needs a combination formula.
Chemical substances are identified by an unordered combination of 3 colors : [Think that you are storing a particular chemical in a bottle. To remember what that substance it you have come up with an idea of coloring it with 3 colors (say, Blue, Green, Yellow). Now if the order would have mattered then, the different cases like when Yellow is written above Blue would have been different from Blue written above yellow. So, in that case we would have been dealing with arrangements of color, So that would have been a good use case for "Permutation".

In the given condition, the order where we write the colors (above/below) doesn't matter as long as they are same, so we are just worried about selecting the 3 colors (not arranging those 3 selected colors), therefore the current case is a proper use case for "Combinations". ]

Hope that helps !

Anurag and anshumishra thank you very much for your reply. The reason why i am getting confused is because of the following sentence in the question:-

If no chemical may be assigned the same 3 colors --> Which means that chemical will be assigned different colors.

And if there are different colors then order does matter, but word "unordered" is mentioned in the question. So, i am taking this as a combination question.

Please clarify whether i am going on a right direction or not.

sachin_yadav wrote:

Anurag@Gurome wrote:
Yes you're correct.
The word unordered means combination. And the combination formula you've given that is also correct and gives the answer 35. May be you've some confusion about what "unordered" means (in that case let me know, I'll explain) or you've made some silly mistake!

Maximum number of substances that can be identified = Number of ways to select 3 colors out of 7 = 7C3 = 7!/(3!*4!) = 35

The correct answer is B.

anshumishra wrote:
You are right, that it needs a combination formula.
Chemical substances are identified by an unordered combination of 3 colors : [Think that you are storing a particular chemical in a bottle. To remember what that substance it you have come up with an idea of coloring it with 3 colors (say, Blue, Green, Yellow). Now if the order would have mattered then, the different cases like when Yellow is written above Blue would have been different from Blue written above yellow. So, in that case we would have been dealing with arrangements of color, So that would have been a good use case for "Permutation".

In the given condition, the order where we write the colors (above/below) doesn't matter as long as they are same, so we are just worried about selecting the 3 colors (not arranging those 3 selected colors), therefore the current case is a proper use case for "Combinations". ]

Hope that helps !

Anurag and anshumishra thank you very much for your reply. The reason why i am getting confused is because of the following sentence in the question:-

If no chemical may be assigned the same 3 colors --> Which means that chemical will be assigned different colors.

And if there are different colors then order does matter, but word "unordered" is mentioned in the question. So, i am taking this as a combination question.

Please clarify whether i am going on a right direction or not.

If no chemical may be assigned the same 3 colors --> Which means that chemical will be assigned different colors.

which means (The better wording should be) no two chemicals may be assigned the same combination of 3 colors - Right here you should have concluded it is a combination problem.

And if there are different colors then order does matter, but word "unordered" is mentioned in the question. So, i am taking this as a combination question.

- It is another big hint which suggests that it is a combination problem.