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Multiple Decision Combinatorics

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Multiple Decision Combinatorics

by pchun008 » Tue May 06, 2014 8:15 pm
The yearbook committee has to pick a color scheme for this year's yearbook. There are 7 colors to choose from (red, orange, yellow, green, blue, indigo, violet). How many different color schemes are possible if the committee can select at most 2 colors?

Can anyone explain simply how to go about solving this problem? (from the strategy guide from MGMAT)

Official Answer: 28
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by Brent@GMATPrepNow » Tue May 06, 2014 8:51 pm
pchun008 wrote:The yearbook committee has to pick a color scheme for this year's yearbook. There are 7 colors to choose from (red, orange, yellow, green, blue, indigo, violet). How many different color schemes are possible if the committee can select at most 2 colors?

Can anyone explain simply how to go about solving this problem? (from the strategy guide from MGMAT)
There are two cases to consider:
1 color
2 colors

1 color
There are 7 colors to choose from, so there are 7 one-color color schemes

2 colors
We must choose 2 colors from 7 colors.
Since the order of the selected colors does not matter, we can use combinations.
We can select 2 colors from 7 colors in 7C2 ways (= 21 ways)
So, there are 21 two-color color schemes

Aside: If anyone is interested, we have a free video on calculating combinations (like 7C2) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

So, the total number of color schemes = 7 + 21 = 28

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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