Let $A= \{1,2,3,4,5,6,7,8,9,0,20,30,40,50\}$. 1. How many subsets of size 2 are there? 2.How many subsets are there altogether? 
Let $A= \{1,2,3,4,5,6,7,8,9,0,20,30,40,50\}$.
  1. How many subsets of size $2$ are there? 
  2.How many subsets are there altogether?

Answer: 
1) I think there are $7$ subsets of size two are there, since $14$ elements$/2=7$ and also by grouping them into pairs it shows there are $7$ groups of pairs as follows; $\{\{1,2\}, \{3,4\}, \{5,6\}, \{7,8\}, \{9,0\}, \{20,30\}, \{40,50\}\}$
2) I choose $15$, but I'm not sure.
However, are my answers valid?  Hints are much appreciated.

as Andre noted there are $ \binom{14}{2} $ ways to choose fourteen elements by picking two.  we call this 14 choose 2. it is equal to $\frac{14!}{(12!)(2!)}$ check out Binomial Coefficient for more
the second part. is achieved by summing $ \binom{14}{n} $  from $n = 0$ to $n = 14$. it is Also the power set see Power Set and it has $2^{14}$ elements. 
