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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