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Permutation and Combinations

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Permutation and Combinations

by akash singhal » Thu Nov 12, 2015 2:55 am
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?


ans 7C3

How to find whether we have to use purmutation or combination in this question?
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by GMATGuruNY » Thu Nov 12, 2015 3:04 am
akash singhal wrote: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 phrase in red implies that the ORDER of the colors does not matter:
ABC is considered the same combination of 3 colors as BCA.

Number of options for the first color = 7.
Number of options for the second color = 6.
Number of options for the third color = 5.
To combine these options, we multiply:
7*6*5.
Since the order of the 3 colors does not matter -- ABC is considered the same combination of 3 colors as BCA -- we divide by the number of ways the 3 colors can be arranged (3!):
(7*6*5)/(3*2*1) = 35.

The approach above can also be represented as 7C3 = 35.
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