Ok, I need someone who understands permutations.

Question

anonymous · Answer

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.

anonymous · Answer

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.