Lottery Calculations

The EuroMillions has five numbers from 1 to 50 and two from 1 to 9.  When the first ball comes up this week, it has a 5 in 50 chance of matching one of the winning numbers from last week.  The odds are that this will happen once every ten lotteries.  Now the next ball has a 4 in 49 chance of matching one of the remaining numbers from last week.  It's 4 in 49 because the first ball removed one of the possibilities.  Multiply 5 over 50 by 4 over 49 and you will find that two numbers from this week's lotto will match last weeks lotto once every 123 draws.  Continue on like this and the final calculation is:

(5/50) * (4/49) * (3/48) * (2*47) * (1/46) * (2/9) * (1/8)

which yields an answer that the lotto number this week will all be the same as last week once every 76,275,360 draws.