Say for example, you had six socks. You wanted to find out how many different pairs you could make out of them. Say x sock was paired with x, then it was paired with y and z. Repeat. The answer is how many different ways you can pair them. What is this called? And how can you find out the answer if you have 65 socks? Thanks!
Responses (1)
Usually this type of math is categorized as combinations (permutations if the order of pairing matters) and they live a happy life in the genre of statistics.
To pair 65 items in any possible combination, you can imagine first taking one sock and pairing it with all the other socks, this makes 64 combinations, then you remove that sock as it as already been combined with all other socks and it can not appear again. Now you have 64 socks and you again pick one sock and do the same thing over until all 63 pairs have been tried. You can do this until you have 2 socks left, giving you only 1 combination.
So what is the sum of 64+63+62+61+...+3+2+1 ? Well you can either just add it all up or use what is called a Gauss method of sums.
With that method you first take the highest number and divide by 2.
The outcome from that you multiply with the number that comes from taking the highest number again and adding 1 more.
In our case we take 64 first and divide by 2, giving us 32.
Then we take the 64 again and add 1 to it, giving us 65.
Then we multiply those two numbers 32 x 65 = 2080
So we have just calculated that with 65 different socks we can make 2080 different combinations.