Factorials in real life. Really.

I finished Charlotte's afghan just in time for my parents to cram it into a suitcase and take it with them when they visited a few weeks ago. She loves it, apparently, and one of these times I'll post pictures. It turned out to be really pretty and weaving in all the loose ends (lots of stripes on this one) was totally worth it. :)

Now I'm working on a small granny square project using a selection of Vanna's Choice yarns in lovely earth tones. My little squares are about 4" and have three rounds of different colors. My sister, who is very smart, challenged me to choose yarn colors as randomly as possible and use whatever I grabbed out of the bag I was keeping the skeins in. So far, it's worked. The colors are very complimentary to each other, and while there are some combinations I wouldn't have purposely chosen, they still look really great. It's been a fun challenge!

I was curious how many combinations were possible with seven colors of yarn and three rounds in each square, and I remembered there was a mathematical formula for figuring things like that out. I couldn't remember the exact formula, though, until I asked my Illustrious Father, who reminded me of factorials.

Factorials! Yes! I always liked factorials, and when Illustrious Father reminded me how they worked, we figured out that seven colors of yarn and three rounds in each square would be 7!/3! which is 7x6x5x4 = 840 possible combinations. This means that my odds of repeating any given combination are VERY slim, which is great. It'll be a lovely little random patchwork afghan and I can't wait to see what it looks like!

I actually think my chances of repeating are a little higher than they would be if I had assigned each yarn a number and rolled dice for each round, but it's still very unlikely that there will be a single repeat.

Yes. If math had been this fun in the classroom, I'd probably have paid more attention and done better...