How to calculate overall odds from a set of individual odds?

Question

Most lottery web sites include overall odds for a combination of odds for a particular game. For example Washington State Lotto has the following: 6 numbers = 1: 6,991,908; 5 numbers = 1: 27,100; 4 numbers = 1: 516; 3 numbers = 1: 28; Overall Odds = 1: 27. How is the last number (1: 27) calculated?

Answer 1

ahhh combinatorics... my favorite.... lets see.

number of ways to win stuff pick 6,5,4, or 3... thats 4 ways to win... I believe the thing to do is add them up (calculated on MS Windows Calculator accessory)...

1/6991908 + 1/27100 + 1/516 + 1/28 =

0.037689313601890275700691831535706

compared to the overall odds of

1/27 = 0.037037037037037037037037037037037

well it seems that adding up the specific odds seems to have gotten a pretty close value to the stated general odds value... I think thats the way its done... could be that my MS Calculator doesnt give precise results for those big number division problem and thats probably where the descrepency comes from.