World!Of
Numbers

WON plate
72 |

[ March 8, 2007 ]
Kanisher Caldwell's (email) combinatorial problem.

In how many ways can you arrange the numbers 1-56 in packs of six ?

Example, without the numbers repeating themselves, i.e.
{1,2,3,4,5,6}
{1,6,7,9,33,42}
{...}

If the order is taken into account,
and e.g. {1,6,7,9,33,42} {1,33,42,9,6,7} which
are two different but equally valid groups,
how does that reflect in the final count ?

Maybe this story is already a partial solution to your problem :

The formula to calculate your chances to win the belgian lottery with
42 numbers (n) and having all six (m) numbers correct is as follows

 n! (n-m)! . m!

or 42! / (36!*6!) =
(1,4050_*10^51) / ((3,7199_*10^41) * (720)) =
So you have 1 chance in 5245786 to win with one grid !

Redoing the exercice for the euromillions lottery is
just a bit more elaborated. The grid contains 50 numbers of which
5 need to be correct and then there are two stars from nine
which have to correspond as well.

 50! (50-5)! . 5! * 9! (9-2)! . 2!

The left part of the equation amounts to 2118760
and the right side equals 36, so in total you have
1 chance in 76275360 to win the euromillions.

This is 14,5 times less than the regular lottery...
now I know where to participate and try my luck.

A000072 Prime Curios! Prime Puzzle
Wikipedia 72 Le Nombre 72 Numberland 72
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