## anonymous 4 years ago Ok, I need someone who understands permutations.

1. anonymous

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.

2. anonymous

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.