Question : Combinations

This question is nothing to do with perl, but perl programmers are the smartest people around so I thought I might as well ask it here.

I need someone to verify my maths in calculating the probability of winning a lottery game. There are 2 barrels, each with 45 numbered balls. 5 balls are selected from barrel A, and 1 ball is selected from barrel B. To win, you must correct pick all 6 balls.

The probability of winning as claimed by the organisers is about 1 in 50 million, but my calculations give 1 in 6 billion! (6,597,498,600 to be precise).

Have I missed something, or are they lying about the odds?

Answer : Combinations

ok, so what's about my answer?