The probability of winning first division Lotto in NZ can easily be calculated by working out the number of possible combinations using factorials as follows:

Number of possible combinations with six balls = 40! / (34! * 6!)

= (40 * 39 * 38 * 37 * 36 * 35) / (6 * 5 * 4 * 3 * 2 * 1) (since 35 * 34 * 33 … on the top and bottom cancel out)

= 3,838,380

So there is one chance in 3,838,380 of winning first division lotto. However if you buy ten lines of lotto, the probability will become one in 383,838.