Quote:
Originally Posted by nickthegeek
The probability of hitting 3 numbers is:
C(44,3)/C(47,6) ~ 0.001233426
Fair odds are around 810/1.
In the formula above, C(n,k) is the number of different ways (combinations) you can pick k elements from a set of n elements. The denominator represents how many possible six-numbers draw you can have. The numerator are your favourable cases: in order to win, the draw must contain your three numbers plus any three from the remaining 44.
Thanks very much for the explanation. I had been trying different methods using the combination formula but it never occurred to me to express it as you did. The bookmaker certainly has a large edge on such bets!