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A sock drawer contains seven socks, each one a different solid color.

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A sock drawer contains seven socks, each one a different solid color.  [#permalink]

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New post 19 Aug 2016, 03:14
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A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?

A. 12
B. 15
C. 21
D. 36
E. 42

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Re: A sock drawer contains seven socks, each one a different solid color.  [#permalink]

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New post 19 Aug 2016, 04:29
Bunuel wrote:
A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?

A. 12
B. 15
C. 21
D. 36
E. 42


Since here order of socks is not important then we'll have 7C2 i.e. 21 combinations.

If order is important then we would have got 42 socks...

IMO option C is correct answer..

OA please...will correct if I missed anything..
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Re: A sock drawer contains seven socks, each one a different solid color.  [#permalink]

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New post 19 Aug 2016, 05:10
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Bunuel wrote:
A sock drawer contains seven socks, each one a different solid color. The colors of the socks are red, orange, yellow, green, blue, indigo, and violet. If a person reaches into the drawer and pulls out two socks, how many different color combinations are possible in the selected pair of socks?

A. 12
B. 15
C. 21
D. 36
E. 42


Since the order in which we select the socks does not matter (e.g., selecting a red sock and then a blue sock is the same outcome as selecting a blue sock and then a red sock), we can use combinations.

We can select 2 socks from 7 socks in 7C2 ways.
7C2 = 21

Answer:

If anyone is interested, we have a video on calculating combinations (like 7C2) in your head:

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A sock drawer contains seven socks, each one a different solid color.  [#permalink]

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New post 19 Aug 2016, 05:22
First socks can be any of the 7 colors AND second socks can be any of the six colors

=> 7 * 6 = 42

Same pair of colors is counted two times. meaning the above has R + G and G + R counted as two different selections.

Therefore answer is half of 42 => 21

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A sock drawer contains seven socks, each one a different solid color.   [#permalink] 19 Aug 2016, 05:22
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