Permutations : A person picks 4 numbers from a set of 9, what are the total ways he can Win? In a casino, a person picks 4 numbers from a set of 9 numbers (3 Even, 6 Odd). A person wins if at least one of those 4 numbers is Even. What are the total ways he can Win ?
There are two approches I believe.
1)  One is to find all possible ways of picking 4 from 9 (9C4) and subtract the number of ways of getting only odd (6C4) ie:
9C4 - 6C4 

2) Pick one even from the set of 3 Evens and pick 3 from the remaning 8. ie :
3C1 * 8C3

What is the difference between the above two, In my oppinon the 2nd method does the same, why is it wronge ?

The problem is that in the second method you are marking one specific odd element in each set. So the combinations which have more than one odd number are counted more than once.
