probability problem help

[mchrism]

Test Panel Selection
A sample of 4 persons is selected for a test from a group containing 10 smokers and 20 nonsmokers. In how many ways can the 4 persons be selected?

can someone please show me how to do this problem thank you, i really have no idea how to approach these two problems



How many non-empty subsets with an even number of elements does a set with 10 elements have?

 

[pka]

Test Panel Selection
A sample of 4 persons is selected for a test from a group containing 10 smokers and 20 nonsmokers. In how many ways can the 4 persons be selected?

\(\displaystyle \sum\limits_{k = 0}^4 {\binom{10}{k}\binom{20}{4-k}}\)

How many non-empty subsets with an even number of elements does a set with 10 elements have?

\(\displaystyle \sum\)\(\displaystyle \limits_{k = 1}^5 \binom{10}{2k} \)