At a certain laboratory....

[dddanny2006]

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

The answer is 35 7c3 =35

However my doubt is that in the questions its not given whether the colors can be repeated or not.They've said that no chemical may be assigned the same color,what this means is that the chemicals cant have same color.For example if Hydrochloric acid is identified by a Red,Green,Blue combination,then Sulphuric acid cant be represented by the same.

The sentence in bold by no way means that the colors cant be repeated.Hence my answer was 7*7*7

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Hi dddanny2006,

You bring up an interesting point: the way that the question is worded does not remove the possibility of 2 (or even 3) of the colors being the SAME color.

The "intent" of the question is that you're supposed to calculate the number of different sets of 3 that can be made from a group of 7. The question uses the phrase "unordered combination", so we'd use the combination formula.

Thus 7c3 = 7! / [3!4!] = 35 sets

IF you allow for a color to be duplicated in a set of 3, then the math becomes a bit more complicated, as you have to consider 3 possible calculations:

3 different colors = 35 sets (using the above equation)

2 colors, 1 duplicate: this can be calculated in a number of different ways; here's an easy way: 7x1x6 = 42 sets

1 color for all 3: 7 sets

35 + 42 + 7 = 84 options
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If the question told you that the combinations were ORDERED and that duplicate colors WERE ALLOWED, then the answer would be 7x7x7 = 343

GMAT assassins aren't born, they're made,
Rich

[dddanny2006]

I dont understand.Why is it 7C3? The problem tells us that different chemicals cant have the same colors,but doesnt tell us whether the colors can be repeated or not in each chemicals case.

For example if Sulphuric acid is represented by Green,Blue,White..then Green blue white cant represent Hydrochloric acid.-------Question makes this clear

But the question it doesnt make it clear whether Sulphuric acid can be represented by Green,Green,Green or Green,Red,Red.

Im struglling in understanding the 7C3.Please explain BTG members.

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Hi dddanny2006,

Maybe I didn't properly mention this in my prior post, but I agree that the question is poorly worded (because it doesn't specifically state that a chemical must be represented by 3 different colors). Since the provided solution is 7c3, then the writer probably "intended" that each chemical be represented by 3 different colors, with no duplicates.

Now, what IF the question had stated that the 3 colors must be different. With that extra piece of information, would you be comfortable with the 7c3 solution?

GMAT assassins aren't born, they're made,
Rich

[dddanny2006]

Thats fine.Thanks Rich.

Hi dddanny2006,

Maybe I didn't properly mention this in my prior post, but I agree that the question is poorly worded (because it doesn't specifically state that a chemical must be represented by 3 different colors). Since the provided solution is 7c3, then the writer probably "intended" that each chemical be represented by 3 different colors, with no duplicates.

Now, what IF the question had stated that the 3 colors must be different. With that extra piece of information, would you be comfortable with the 7c3 solution?

GMAT assassins aren't born, they're made,
Rich