From the BBC:

**Bulgarian lottery repeat probed**

The Bulgarian authorities have ordered an investigation after the same six numbers were drawn in two consecutive rounds of the national lottery.

A mathematician said the chance of the same six numbers coming up twice in a row was one in four million. But he said coincidences did happen.

Not sure where the said mathematician got 4m-to-1 from. I did a bit of digging (googling, mainly), and found out that the Bulgarian lottery plays 42 numbers, and draws six.

Under the above conditions, the chance of a particular set of six numbers appearing is:

1/(42*41*40*39*38*37)/(6*5*4*3*2*1) = 1/5.2m

For two identical sets of numbers to come up twice, the chance of that happening is simply the chance of a particular set of numbers coming up.

I therefore argue that the chance of two identical sets of numbers coming up twice in a row is 1 in 5.2 million. Am I right or am I missing something here?

Sounds about as unlikely as you returning to The Filter^ regularly!!

Posted by: aje | September 18, 2009 at 11:27 AM

Given that the two sets of numbers have already turned up twice then the probability is 1

Posted by: Tim Worstall | September 19, 2009 at 10:56 AM

42!/(6!*36!) = 5,245,786

But to get that same combination twice in a row it would be 5.2m^2 right?

Posted by: aje | September 19, 2009 at 12:17 PM