Lottery questions

[kenny1999]

6 balls are drawn from a total of 49 balls randomly. Order does not matter, as long as 6 balls are matched, first prize is won, what is the probability of winning the first prize?

Another question is horse racing. For certain three matches, which may have 10 to 14 horses in total, different horses may have different conditions and abilities so the winning odds of each horse may not be as simple as 1/10 or 1/14. You choose three horses from each of the three matches so you are choosing 9 horses in total, if all 9 horses in three matches finish for the 1st, 2nd and 3rd place, order isn't counted, i.e. ABC, ACB, BAC, BCA, CAB, CBA don't matter.), then you win the jackpot, what is the probability of winning the jackpot? Since number of horses in a match may vary, conditions of horses in a match may vary, I'd like to know how to work it out, rather than the final answers alone.)

[Genady]

Homework in combinatorics?