Numbers / The anaesthetist

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The numerical story of the week has been that of a man taking Camelot to court for allegedly miscalculating the odds of winning a pounds 10 prize on the lottery. They say the odds are 56 to 1; he says 1132 to 1.

Let's count. There are 49 balls in the draw. So there are 49 ways to pick the first ball, leaving 48 for the second, 47 for the third and so on. Which gives us 49x48x47x46x45x44 possible lottery draws (ignoring the bonus number). But this takes into account the order in which the balls are drawn. Each six-pack of numbers has in fact been counted 6x5x4x3x2 times - the number of way of permuting six objects. So the number of possible draws is: 49x48x47x46x45x44/6x5x4x3x2 which equals 13,983,816.

Now we must count how many of those 13,983,816 have exactly three numbers in common with the six on our card. We must multiply together the number of ways of picking three numbers from the six on our card (=6x5x4/3x2) with the ways of picking three numbers from the 43 not on our card (=43x42x41/3x2). Which comes out as 20x12341 = 246820.

So the total chance of winning is 246,820 in 13,983,816 or 1 in 56.6559, which is pretty close to what Camelot said in the first place. So that is probably how they did their calculation. We do not know how the man who took them to court did his sums.

COMPETITION: Back to our "26 L of the A" (Letters of the Alphabet) style with three Chambers Dictionary prizes for correct disentanglings.

2 F in a R G

4 J A I D

6 O T B

8 N in an O

10 S-S and A T

Entries, by 27 June, to: Numbers, the Independent, 1 Canada Square, Canary Wharf, London E14 5DL.

2 June competition report

10 Bo Derek and Dudley Moore Film; 100 Acre Wood Where Winnie the Pooh Lived; 1000 Words a Picture is Worth; 1000 Guineas Horserace at Newmarket; 1,000,000 Miles I'd Walk for One of Your Smiles. Prizes: Arthur Johnson, M Lavender, Mrs PJ Pinder.

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