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# How many color combinations are possible?

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cmthmpsn
Member
Joined: 21 Jun 2012
Posts: 32
Location: Ontario, Oregon, USA
How many color combinations are possible?     Reply with quote
 4:55 pm Dec 19, 2015

Nope, not asking anyone to find out, I remembered from my statistics class that the formula involved some factorials (major math stuff), but I didn't remember the complete formula, so I looked it up online. Then, because it was going to be a huge calculation, I found a site which calculated it for me.

So here's how many possible combinations there are to use 2 strands of DMC floss, given that there are currently 454 colors:

103,285

That's a huge number! I sure hope she doesn't come out with any pattern that uses them all! But, then again, if she did an original fractal-type design, that might be quite beautiful.
boxxy
Newbie
Joined: 27 Sep 2017
Posts: 1
Re: How many color combinations are possible?     Reply with quote
 3:32 pm Sep 28, 2017

I too have taken a statistics class, and I can expand on the math here so everyone can calculate the number on their own and with other amounts of DMC floss.

The formula using factorials for the number of blended colors is nCr = n!/(r!(n-r)!) where n is the number of things, in this case 454 floss colors, and r is the number of strands used at a time, in this case 2.

You can calculate this with a website like wolframalpha.com. Paste n!/(r!(n-r)!) , n = 454, r = 2 and you'll get 102,831. This is only the blended colors. Adding the number of solid colors will get you all possible combinations. The formula would be n!/(r!(n-r)!) + n and the result is 103,285, like in the first post.

There is a much easier way to calculate this and you can use a regular calculator!

Another equation for the amount of blended colors is y = (n^2 - n)/2 where n is number of floss colors and y would be the result. If you want to include solid colors, the equation is y = ((n^2 - n)/2) + n.

A step by step for calculating this on a regular calculator:
454 multiply by 454, get 206,116
subtract 454, get 205,662
divide by 2, get 102,831, which is the number of blended colors.
add 454, get 103,285, the number of combinations that includes blended and solid colors.

If you want to use wolframalpha, paste in ((n^2 - n)/2) + n, n = 454.

Just change the 454 to however many colors you are interested in.

If there are 500 colors, there would be 125,250 resulting combinations including solid colors.
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