Lotto Probabilities based on number of balls chosen I found the formula for working out lotto probabilities on wikipedia to be: $$\frac{\binom {K}{B} \binom {N-K}{K-B}}{\binom {N}{K}}$$ **Where:** $ N = $ The number of balls in the Lotto draw $ K = $ The number of balls on a ticket (and also drawn) $ B = $ The number of matching balls for a winning ticket I would like to modify this to treat $K$ as 2 separate variables, one for the number of balls drawn in the Lotto and one for the number of balls that I have chosen. In other words, how can I work out the probability of getting $B$ numbers correct from my selection of $T$ numbers, out of their selection of $K$ numbers drawn in the lotto, consisting of $N$ balls in total.

Taking it to mean that in a typical 6/49 game, where six numbers are drawn from a range of 49, you choose, say, 10 numbers, and get ,say, 4 of the six numbers drawn correct, i.e. N = 49, K = 6, T=10,B = 4 for this example ?

$Pr = \dfrac{\binom{K}{B}\binom{N-K}{T-B}}{\binom{N}{T}}$