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U.K Lottery
By Anonymous on Saturday, September 23, 2000 - 10:01 pm:

The figure of 14,000,000 to 1 is often quoted as being the odds of winning the lottery. Is this the
correct odds of winning, and how is this calculated?

By Neil Morrison (P1462) on Sunday, September 24, 2000 - 11:10 am:

You need to get the correct six balls (in any order) from 49. Thus:

chance= (6/49)(5/48)(4/47)(3/46)(2/45)(1/44)

= (6!)(43!)/(49!)

= 1/13,983,816

By The Editor:

For those with a little less knowledge of probability:
The probability of thing A happening and thing B happening is found by multiplying the two probabilities. For example, if you toss two coins, the probability of getting heads on the first and heads on the second is ½×½=¼.

When you sit watching the balls coming out of the machine, the probability that the first one is one of your six is 6/49. If it is, there are now 48 balls left, and 5 of them are ones you want, so the probability that the next ball is one of your numbers is 5/48. And so on. Hopefully this explains Neil's formula. His second line uses factorial notation, which may be unfamiliar, but if you multiply the fractions you should get to the answer at the bottom.