Probability of winning first division Lotto in NZ

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.