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.

The total number of subsets of size $2$ is $\binom{14}{2}$. To understand this try to see how many ways are there to pick two distinct elements out of the set.
For the second part using the similar idea from the previous part, there are $\frac{14}{k}$ subsets with size $k$. So the total sum is:
$$\sum_{n=0}^{14} \binom{14}{n} = \sum_{n=0}^{14} \binom{14}{n}(1)^{14-n}(1)^{n} = (1+1)^{14} = 2^{14}$$
