Here's the question you clicked on:
InsertCoolNameHere
Ok, I need someone who understands permutations.
2. The number of permutations of two items from a data set is always two time the number of combinations when taking two objects at a time from the same data set. True or False. Explain why.
True \[nCr = \frac{n!}{(n - r)!r!}\] \[2C2 = \frac{2!}{(2 - 2)!2!}\] \[2C2 = \frac{2!}{0!2!}\] \[2C2 = \frac{2!}{2!}\] \[2C2 = 1\] \[nPr = \frac{n!}{(n - r)!}\] \[2P2 = \frac{2!}{(2 - 2)!}\] \[2P2 = \frac{2!}{0!}\] \[2P2 = 2!\] \[2P2 = 2\] 2 is 2 times 1. THis happens because if order is not important and you're choosing 2 from 2, you get 1. It's only natural that if order is important, you can just switch the order of them around and get 2. The same is if it's 2 choose 1.