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 !